EduSahara™ Assignment
Name : Trigonometric ratios in terms of other ratios
Chapter : Trigonometry
Grade : SSC Grade X
License : Non Commercial Use
Question
1
1.
Express
sin
θ
in terms of
cos
θ
(i)
√
1
−
cos
2
θ
cos
θ
(ii)
1
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
(iv)
cos
θ
√
1
−
cos
2
θ
(v)
1
cos
θ
Question
2
2.
Express
sin
θ
in terms of
tan
θ
(i)
1
tan
θ
(ii)
√
1
+
tan
2
θ
(iii)
√
1
+
tan
2
θ
tan
θ
(iv)
tan
θ
√
1
+
tan
2
θ
(v)
1
√
1
+
tan
2
θ
Question
3
3.
Express
sin
θ
in terms of
cot
θ
(i)
1
√
1
+
cot
2
θ
(ii)
1
cot
θ
(iii)
cot
θ
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
cot
θ
(v)
√
1
+
cot
2
θ
Question
4
4.
Express
sin
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
1
sec
θ
(iii)
√
sec
2
θ
−
1
(iv)
1
√
sec
2
θ
−
1
(v)
√
sec
2
θ
−
1
sec
θ
Question
5
5.
Express
sin
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
(iii)
1
√
cosec
2
θ
−
1
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
1
cosec
θ
Question
6
6.
Express
cos
θ
in terms of
sin
θ
(i)
1
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
sin
θ
(iii)
√
1
−
sin
2
θ
(iv)
1
sin
θ
(v)
sin
θ
√
1
−
sin
2
θ
Question
7
7.
Express
cos
θ
in terms of
tan
θ
(i)
1
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
tan
θ
√
1
+
tan
2
θ
(iv)
1
tan
θ
(v)
√
1
+
tan
2
θ
Question
8
8.
Express
cos
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
(ii)
1
cot
θ
(iii)
1
√
1
+
cot
2
θ
(iv)
cot
θ
√
1
+
cot
2
θ
(v)
√
1
+
cot
2
θ
cot
θ
Question
9
9.
Express
cos
θ
in terms of
sec
θ
(i)
1
√
sec
2
θ
−
1
(ii)
√
sec
2
θ
−
1
(iii)
√
sec
2
θ
−
1
sec
θ
(iv)
sec
θ
√
sec
2
θ
−
1
(v)
1
sec
θ
Question
10
10.
Express
cos
θ
in terms of
cosec
θ
(i)
1
cosec
θ
(ii)
cosec
θ
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
(iv)
1
√
cosec
2
θ
−
1
(v)
√
cosec
2
θ
−
1
cosec
θ
Question
11
11.
Express
tan
θ
in terms of
sin
θ
(i)
1
√
1
−
sin
2
θ
(ii)
sin
θ
√
1
−
sin
2
θ
(iii)
1
sin
θ
(iv)
√
1
−
sin
2
θ
(v)
√
1
−
sin
2
θ
sin
θ
Question
12
12.
Express
tan
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
1
cos
θ
(iv)
cos
θ
√
1
−
cos
2
θ
(v)
√
1
−
cos
2
θ
Question
13
13.
Express
tan
θ
in terms of
cot
θ
(i)
1
√
1
+
cot
2
θ
(ii)
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
cot
θ
(iv)
1
cot
θ
(v)
cot
θ
√
1
+
cot
2
θ
Question
14
14.
Express
tan
θ
in terms of
sec
θ
(i)
1
sec
θ
(ii)
sec
θ
√
sec
2
θ
−
1
(iii)
√
sec
2
θ
−
1
(iv)
√
sec
2
θ
−
1
sec
θ
(v)
1
√
sec
2
θ
−
1
Question
15
15.
Express
tan
θ
in terms of
cosec
θ
(i)
1
√
cosec
2
θ
−
1
(ii)
√
cosec
2
θ
−
1
cosec
θ
(iii)
1
cosec
θ
(iv)
√
cosec
2
θ
−
1
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
16
16.
Express
cot
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
(ii)
sin
θ
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
1
sin
θ
(v)
1
√
1
−
sin
2
θ
Question
17
17.
Express
cot
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
1
cos
θ
(v)
√
1
−
cos
2
θ
cos
θ
Question
18
18.
Express
cot
θ
in terms of
tan
θ
(i)
tan
θ
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
(iii)
√
1
+
tan
2
θ
tan
θ
(iv)
1
tan
θ
(v)
1
√
1
+
tan
2
θ
Question
19
19.
Express
cot
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
√
sec
2
θ
−
1
sec
θ
(iii)
1
√
sec
2
θ
−
1
(iv)
√
sec
2
θ
−
1
(v)
1
sec
θ
Question
20
20.
Express
cot
θ
in terms of
cosec
θ
(i)
1
√
cosec
2
θ
−
1
(ii)
cosec
θ
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
(iv)
1
cosec
θ
(v)
√
cosec
2
θ
−
1
cosec
θ
Question
21
21.
Express
sec
θ
in terms of
sin
θ
(i)
sin
θ
√
1
−
sin
2
θ
(ii)
1
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
√
1
−
sin
2
θ
(v)
1
sin
θ
Question
22
22.
Express
sec
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
1
cos
θ
(iv)
√
1
−
cos
2
θ
(v)
cos
θ
√
1
−
cos
2
θ
Question
23
23.
Express
sec
θ
in terms of
tan
θ
(i)
1
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
√
1
+
tan
2
θ
(iv)
1
tan
θ
(v)
tan
θ
√
1
+
tan
2
θ
Question
24
24.
Express
sec
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
(ii)
√
1
+
cot
2
θ
cot
θ
(iii)
1
cot
θ
(iv)
cot
θ
√
1
+
cot
2
θ
(v)
1
√
1
+
cot
2
θ
Question
25
25.
Express
sec
θ
in terms of
cosec
θ
(i)
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
cosec
θ
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
1
√
cosec
2
θ
−
1
Question
26
26.
Express
cosec
θ
in terms of
sin
θ
(i)
1
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
(iii)
1
sin
θ
(iv)
√
1
−
sin
2
θ
sin
θ
(v)
sin
θ
√
1
−
sin
2
θ
Question
27
27.
Express
cosec
θ
in terms of
cos
θ
(i)
√
1
−
cos
2
θ
cos
θ
(ii)
1
√
1
−
cos
2
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
1
cos
θ
(v)
√
1
−
cos
2
θ
Question
28
28.
Express
cosec
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
1
√
1
+
tan
2
θ
(iii)
1
tan
θ
(iv)
tan
θ
√
1
+
tan
2
θ
(v)
√
1
+
tan
2
θ
tan
θ
Question
29
29.
Express
cosec
θ
in terms of
cot
θ
(i)
1
cot
θ
(ii)
cot
θ
√
1
+
cot
2
θ
(iii)
1
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
cot
θ
(v)
√
1
+
cot
2
θ
Question
30
30.
Express
cosec
θ
in terms of
sec
θ
(i)
1
√
sec
2
θ
−
1
(ii)
sec
θ
√
sec
2
θ
−
1
(iii)
√
sec
2
θ
−
1
sec
θ
(iv)
√
sec
2
θ
−
1
(v)
1
sec
θ
Question
31
31.
Express
sin
45°
in terms of
cos
45°
(i)
cos
45°
√
1
−
cos
2
45°
(ii)
√
1
−
cos
2
45°
(iii)
1
√
1
−
cos
2
45°
(iv)
√
1
−
cos
2
45°
cos
45°
(v)
1
cos
45°
Question
32
32.
Express
sin
65°
in terms of
tan
65°
(i)
√
1
+
tan
2
65°
tan
65°
(ii)
tan
65°
√
1
+
tan
2
65°
(iii)
1
√
1
+
tan
2
65°
(iv)
√
1
+
tan
2
65°
(v)
1
tan
65°
Question
33
33.
Express
sin
59°
in terms of
cot
59°
(i)
cot
59°
√
1
+
cot
2
59°
(ii)
1
√
1
+
cot
2
59°
(iii)
√
1
+
cot
2
59°
cot
59°
(iv)
√
1
+
cot
2
59°
(v)
1
cot
59°
Question
34
34.
Express
sin
37°
in terms of
sec
37°
(i)
√
sec
2
37°
−
1
(ii)
sec
37°
√
sec
2
37°
−
1
(iii)
1
√
sec
2
37°
−
1
(iv)
1
sec
37°
(v)
√
sec
2
37°
−
1
sec
37°
Question
35
35.
Express
sin
55°
in terms of
cosec
55°
(i)
√
cosec
2
55°
−
1
cosec
55°
(ii)
cosec
55°
√
cosec
2
55°
−
1
(iii)
√
cosec
2
55°
−
1
(iv)
1
cosec
55°
(v)
1
√
cosec
2
55°
−
1
Question
36
36.
Express
cos
23°
in terms of
sin
23°
(i)
1
√
1
−
sin
2
23°
(ii)
√
1
−
sin
2
23°
(iii)
sin
23°
√
1
−
sin
2
23°
(iv)
√
1
−
sin
2
23°
sin
23°
(v)
1
sin
23°
Question
37
37.
Express
cos
37°
in terms of
tan
37°
(i)
1
tan
37°
(ii)
√
1
+
tan
2
37°
(iii)
√
1
+
tan
2
37°
tan
37°
(iv)
1
√
1
+
tan
2
37°
(v)
tan
37°
√
1
+
tan
2
37°
Question
38
38.
Express
cos
76°
in terms of
cot
76°
(i)
cot
76°
√
1
+
cot
2
76°
(ii)
√
1
+
cot
2
76°
(iii)
1
cot
76°
(iv)
√
1
+
cot
2
76°
cot
76°
(v)
1
√
1
+
cot
2
76°
Question
39
39.
Express
cos
23°
in terms of
sec
23°
(i)
sec
23°
√
sec
2
23°
−
1
(ii)
√
sec
2
23°
−
1
sec
23°
(iii)
1
√
sec
2
23°
−
1
(iv)
1
sec
23°
(v)
√
sec
2
23°
−
1
Question
40
40.
Express
cos
61°
in terms of
cosec
61°
(i)
cosec
61°
√
cosec
2
61°
−
1
(ii)
√
cosec
2
61°
−
1
(iii)
1
√
cosec
2
61°
−
1
(iv)
1
cosec
61°
(v)
√
cosec
2
61°
−
1
cosec
61°
Question
41
41.
Express
tan
21°
in terms of
sin
21°
(i)
1
sin
21°
(ii)
1
√
1
−
sin
2
21°
(iii)
sin
21°
√
1
−
sin
2
21°
(iv)
√
1
−
sin
2
21°
(v)
√
1
−
sin
2
21°
sin
21°
Question
42
42.
Express
tan
29°
in terms of
cos
29°
(i)
√
1
−
cos
2
29°
cos
29°
(ii)
cos
29°
√
1
−
cos
2
29°
(iii)
1
√
1
−
cos
2
29°
(iv)
√
1
−
cos
2
29°
(v)
1
cos
29°
Question
43
43.
Express
tan
48°
in terms of
cot
48°
(i)
1
cot
48°
(ii)
1
√
1
+
cot
2
48°
(iii)
√
1
+
cot
2
48°
(iv)
cot
48°
√
1
+
cot
2
48°
(v)
√
1
+
cot
2
48°
cot
48°
Question
44
44.
Express
tan
56°
in terms of
sec
56°
(i)
sec
56°
√
sec
2
56°
−
1
(ii)
1
√
sec
2
56°
−
1
(iii)
√
sec
2
56°
−
1
(iv)
1
sec
56°
(v)
√
sec
2
56°
−
1
sec
56°
Question
45
45.
Express
tan
78°
in terms of
cosec
78°
(i)
1
cosec
78°
(ii)
√
cosec
2
78°
−
1
cosec
78°
(iii)
cosec
78°
√
cosec
2
78°
−
1
(iv)
√
cosec
2
78°
−
1
(v)
1
√
cosec
2
78°
−
1
Question
46
46.
Express
cot
53°
in terms of
sin
53°
(i)
sin
53°
√
1
−
sin
2
53°
(ii)
1
sin
53°
(iii)
1
√
1
−
sin
2
53°
(iv)
√
1
−
sin
2
53°
(v)
√
1
−
sin
2
53°
sin
53°
Question
47
47.
Express
cot
38°
in terms of
cos
38°
(i)
1
cos
38°
(ii)
√
1
−
cos
2
38°
(iii)
cos
38°
√
1
−
cos
2
38°
(iv)
√
1
−
cos
2
38°
cos
38°
(v)
1
√
1
−
cos
2
38°
Question
48
48.
Express
cot
66°
in terms of
tan
66°
(i)
√
1
+
tan
2
66°
(ii)
1
tan
66°
(iii)
1
√
1
+
tan
2
66°
(iv)
tan
66°
√
1
+
tan
2
66°
(v)
√
1
+
tan
2
66°
tan
66°
Question
49
49.
Express
cot
57°
in terms of
sec
57°
(i)
1
√
sec
2
57°
−
1
(ii)
√
sec
2
57°
−
1
(iii)
1
sec
57°
(iv)
√
sec
2
57°
−
1
sec
57°
(v)
sec
57°
√
sec
2
57°
−
1
Question
50
50.
Express
cot
53°
in terms of
cosec
53°
(i)
1
cosec
53°
(ii)
cosec
53°
√
cosec
2
53°
−
1
(iii)
1
√
cosec
2
53°
−
1
(iv)
√
cosec
2
53°
−
1
cosec
53°
(v)
√
cosec
2
53°
−
1
Question
51
51.
Express
sec
39°
in terms of
sin
39°
(i)
sin
39°
√
1
−
sin
2
39°
(ii)
1
√
1
−
sin
2
39°
(iii)
√
1
−
sin
2
39°
(iv)
1
sin
39°
(v)
√
1
−
sin
2
39°
sin
39°
Question
52
52.
Express
sec
54°
in terms of
cos
54°
(i)
1
cos
54°
(ii)
1
√
1
−
cos
2
54°
(iii)
√
1
−
cos
2
54°
(iv)
√
1
−
cos
2
54°
cos
54°
(v)
cos
54°
√
1
−
cos
2
54°
Question
53
53.
Express
sec
71°
in terms of
tan
71°
(i)
tan
71°
√
1
+
tan
2
71°
(ii)
√
1
+
tan
2
71°
(iii)
1
√
1
+
tan
2
71°
(iv)
1
tan
71°
(v)
√
1
+
tan
2
71°
tan
71°
Question
54
54.
Express
sec
73°
in terms of
cot
73°
(i)
1
√
1
+
cot
2
73°
(ii)
cot
73°
√
1
+
cot
2
73°
(iii)
√
1
+
cot
2
73°
cot
73°
(iv)
1
cot
73°
(v)
√
1
+
cot
2
73°
Question
55
55.
Express
sec
74°
in terms of
cosec
74°
(i)
1
√
cosec
2
74°
−
1
(ii)
1
cosec
74°
(iii)
cosec
74°
√
cosec
2
74°
−
1
(iv)
√
cosec
2
74°
−
1
cosec
74°
(v)
√
cosec
2
74°
−
1
Question
56
56.
Express
cosec
74°
in terms of
sin
74°
(i)
√
1
−
sin
2
74°
sin
74°
(ii)
1
sin
74°
(iii)
√
1
−
sin
2
74°
(iv)
1
√
1
−
sin
2
74°
(v)
sin
74°
√
1
−
sin
2
74°
Question
57
57.
Express
cosec
34°
in terms of
cos
34°
(i)
1
cos
34°
(ii)
cos
34°
√
1
−
cos
2
34°
(iii)
√
1
−
cos
2
34°
cos
34°
(iv)
1
√
1
−
cos
2
34°
(v)
√
1
−
cos
2
34°
Question
58
58.
Express
cosec
38°
in terms of
tan
38°
(i)
1
√
1
+
tan
2
38°
(ii)
√
1
+
tan
2
38°
(iii)
√
1
+
tan
2
38°
tan
38°
(iv)
tan
38°
√
1
+
tan
2
38°
(v)
1
tan
38°
Question
59
59.
Express
cosec
65°
in terms of
cot
65°
(i)
1
√
1
+
cot
2
65°
(ii)
√
1
+
cot
2
65°
(iii)
√
1
+
cot
2
65°
cot
65°
(iv)
1
cot
65°
(v)
cot
65°
√
1
+
cot
2
65°
Question
60
60.
Express
cosec
74°
in terms of
sec
74°
(i)
1
sec
74°
(ii)
sec
74°
√
sec
2
74°
−
1
(iii)
1
√
sec
2
74°
−
1
(iv)
√
sec
2
74°
−
1
sec
74°
(v)
√
sec
2
74°
−
1
Assignment Key
1) (iii)
2) (iv)
3) (i)
4) (v)
5) (v)
6) (iii)
7) (i)
8) (iv)
9) (v)
10) (v)
11) (ii)
12) (ii)
13) (iv)
14) (iii)
15) (i)
16) (iii)
17) (iii)
18) (iv)
19) (iii)
20) (iii)
21) (ii)
22) (iii)
23) (iii)
24) (ii)
25) (iv)
26) (iii)
27) (ii)
28) (v)
29) (v)
30) (ii)
31) (ii)
32) (ii)
33) (ii)
34) (v)
35) (iv)
36) (ii)
37) (iv)
38) (i)
39) (iv)
40) (v)
41) (iii)
42) (i)
43) (i)
44) (iii)
45) (v)
46) (v)
47) (iii)
48) (ii)
49) (i)
50) (v)
51) (ii)
52) (i)
53) (ii)
54) (iii)
55) (iii)
56) (ii)
57) (iv)
58) (iii)
59) (ii)
60) (ii)
