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
(ii)
1
cos
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
cos
θ
(v)
1
√
1
−
cos
2
θ
Question
2
2.
Express
sin
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
tan
θ
(ii)
1
tan
θ
(iii)
√
1
+
tan
2
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
+
cot
2
θ
cot
θ
(ii)
√
1
+
cot
2
θ
(iii)
cot
θ
√
1
+
cot
2
θ
(iv)
1
√
1
+
cot
2
θ
(v)
1
cot
θ
Question
4
4.
Express
sin
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
sec
θ
(ii)
1
√
sec
2
θ
−
1
(iii)
sec
θ
√
sec
2
θ
−
1
(iv)
1
sec
θ
(v)
√
sec
2
θ
−
1
Question
5
5.
Express
sin
θ
in terms of
cosec
θ
(i)
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
cosec
θ
(iii)
√
cosec
2
θ
−
1
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
1
√
cosec
2
θ
−
1
Question
6
6.
Express
cos
θ
in terms of
sin
θ
(i)
1
sin
θ
(ii)
√
1
−
sin
2
θ
sin
θ
(iii)
√
1
−
sin
2
θ
(iv)
1
√
1
−
sin
2
θ
(v)
sin
θ
√
1
−
sin
2
θ
Question
7
7.
Express
cos
θ
in terms of
tan
θ
(i)
1
tan
θ
(ii)
tan
θ
√
1
+
tan
2
θ
(iii)
1
√
1
+
tan
2
θ
(iv)
√
1
+
tan
2
θ
tan
θ
(v)
√
1
+
tan
2
θ
Question
8
8.
Express
cos
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
cot
θ
(ii)
√
1
+
cot
2
θ
(iii)
1
√
1
+
cot
2
θ
(iv)
1
cot
θ
(v)
cot
θ
√
1
+
cot
2
θ
Question
9
9.
Express
cos
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
1
√
sec
2
θ
−
1
(iii)
√
sec
2
θ
−
1
(iv)
1
sec
θ
(v)
√
sec
2
θ
−
1
sec
θ
Question
10
10.
Express
cos
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
(ii)
1
√
cosec
2
θ
−
1
(iii)
1
cosec
θ
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
√
cosec
2
θ
−
1
cosec
θ
Question
11
11.
Express
tan
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
(ii)
1
sin
θ
(iii)
1
√
1
−
sin
2
θ
(iv)
sin
θ
√
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
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
cos
θ
(v)
√
1
−
cos
2
θ
Question
13
13.
Express
tan
θ
in terms of
cot
θ
(i)
1
cot
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
cot
θ
(v)
cot
θ
√
1
+
cot
2
θ
Question
14
14.
Express
tan
θ
in terms of
sec
θ
(i)
1
√
sec
2
θ
−
1
(ii)
sec
θ
√
sec
2
θ
−
1
(iii)
1
sec
θ
(iv)
√
sec
2
θ
−
1
(v)
√
sec
2
θ
−
1
sec
θ
Question
15
15.
Express
tan
θ
in terms of
cosec
θ
(i)
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
(iii)
1
√
cosec
2
θ
−
1
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
√
cosec
2
θ
−
1
cosec
θ
Question
16
16.
Express
cot
θ
in terms of
sin
θ
(i)
1
√
1
−
sin
2
θ
(ii)
1
sin
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
sin
θ
√
1
−
sin
2
θ
(v)
√
1
−
sin
2
θ
Question
17
17.
Express
cot
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
cos
θ
√
1
−
cos
2
θ
(iii)
1
cos
θ
(iv)
√
1
−
cos
2
θ
cos
θ
(v)
√
1
−
cos
2
θ
Question
18
18.
Express
cot
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
tan
θ
√
1
+
tan
2
θ
(iii)
√
1
+
tan
2
θ
tan
θ
(iv)
1
√
1
+
tan
2
θ
(v)
1
tan
θ
Question
19
19.
Express
cot
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
(ii)
√
sec
2
θ
−
1
sec
θ
(iii)
1
sec
θ
(iv)
sec
θ
√
sec
2
θ
−
1
(v)
1
√
sec
2
θ
−
1
Question
20
20.
Express
cot
θ
in terms of
cosec
θ
(i)
1
√
cosec
2
θ
−
1
(ii)
1
cosec
θ
(iii)
√
cosec
2
θ
−
1
cosec
θ
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
√
cosec
2
θ
−
1
Question
21
21.
Express
sec
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
sin
θ
(ii)
√
1
−
sin
2
θ
(iii)
sin
θ
√
1
−
sin
2
θ
(iv)
1
√
1
−
sin
2
θ
(v)
1
sin
θ
Question
22
22.
Express
sec
θ
in terms of
cos
θ
(i)
√
1
−
cos
2
θ
(ii)
1
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
cos
θ
(iv)
cos
θ
√
1
−
cos
2
θ
(v)
1
cos
θ
Question
23
23.
Express
sec
θ
in terms of
tan
θ
(i)
1
√
1
+
tan
2
θ
(ii)
1
tan
θ
(iii)
√
1
+
tan
2
θ
(iv)
tan
θ
√
1
+
tan
2
θ
(v)
√
1
+
tan
2
θ
tan
θ
Question
24
24.
Express
sec
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
cot
θ
(ii)
cot
θ
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
(iv)
1
√
1
+
cot
2
θ
(v)
1
cot
θ
Question
25
25.
Express
sec
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
26
26.
Express
cosec
θ
in terms of
sin
θ
(i)
1
sin
θ
(ii)
1
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
(iv)
sin
θ
√
1
−
sin
2
θ
(v)
√
1
−
sin
2
θ
sin
θ
Question
27
27.
Express
cosec
θ
in terms of
cos
θ
(i)
cos
θ
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
1
cos
θ
(iv)
1
√
1
−
cos
2
θ
(v)
√
1
−
cos
2
θ
Question
28
28.
Express
cosec
θ
in terms of
tan
θ
(i)
tan
θ
√
1
+
tan
2
θ
(ii)
1
√
1
+
tan
2
θ
(iii)
√
1
+
tan
2
θ
tan
θ
(iv)
√
1
+
tan
2
θ
(v)
1
tan
θ
Question
29
29.
Express
cosec
θ
in terms of
cot
θ
(i)
cot
θ
√
1
+
cot
2
θ
(ii)
1
cot
θ
(iii)
√
1
+
cot
2
θ
cot
θ
(iv)
1
√
1
+
cot
2
θ
(v)
√
1
+
cot
2
θ
Question
30
30.
Express
cosec
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
(ii)
1
sec
θ
(iii)
1
√
sec
2
θ
−
1
(iv)
sec
θ
√
sec
2
θ
−
1
(v)
√
sec
2
θ
−
1
sec
θ
Question
31
31.
Express
sin
42°
in terms of
cos
42°
(i)
1
√
1
−
cos
2
42°
(ii)
1
cos
42°
(iii)
√
1
−
cos
2
42°
cos
42°
(iv)
cos
42°
√
1
−
cos
2
42°
(v)
√
1
−
cos
2
42°
Question
32
32.
Express
sin
74°
in terms of
tan
74°
(i)
√
1
+
tan
2
74°
(ii)
√
1
+
tan
2
74°
tan
74°
(iii)
tan
74°
√
1
+
tan
2
74°
(iv)
1
√
1
+
tan
2
74°
(v)
1
tan
74°
Question
33
33.
Express
sin
58°
in terms of
cot
58°
(i)
cot
58°
√
1
+
cot
2
58°
(ii)
√
1
+
cot
2
58°
(iii)
1
cot
58°
(iv)
1
√
1
+
cot
2
58°
(v)
√
1
+
cot
2
58°
cot
58°
Question
34
34.
Express
sin
51°
in terms of
sec
51°
(i)
1
sec
51°
(ii)
√
sec
2
51°
−
1
(iii)
√
sec
2
51°
−
1
sec
51°
(iv)
sec
51°
√
sec
2
51°
−
1
(v)
1
√
sec
2
51°
−
1
Question
35
35.
Express
sin
34°
in terms of
cosec
34°
(i)
cosec
34°
√
cosec
2
34°
−
1
(ii)
1
√
cosec
2
34°
−
1
(iii)
√
cosec
2
34°
−
1
cosec
34°
(iv)
1
cosec
34°
(v)
√
cosec
2
34°
−
1
Question
36
36.
Express
cos
20°
in terms of
sin
20°
(i)
1
√
1
−
sin
2
20°
(ii)
sin
20°
√
1
−
sin
2
20°
(iii)
1
sin
20°
(iv)
√
1
−
sin
2
20°
sin
20°
(v)
√
1
−
sin
2
20°
Question
37
37.
Express
cos
65°
in terms of
tan
65°
(i)
tan
65°
√
1
+
tan
2
65°
(ii)
1
tan
65°
(iii)
√
1
+
tan
2
65°
tan
65°
(iv)
√
1
+
tan
2
65°
(v)
1
√
1
+
tan
2
65°
Question
38
38.
Express
cos
62°
in terms of
cot
62°
(i)
1
cot
62°
(ii)
cot
62°
√
1
+
cot
2
62°
(iii)
√
1
+
cot
2
62°
cot
62°
(iv)
1
√
1
+
cot
2
62°
(v)
√
1
+
cot
2
62°
Question
39
39.
Express
cos
31°
in terms of
sec
31°
(i)
1
sec
31°
(ii)
1
√
sec
2
31°
−
1
(iii)
√
sec
2
31°
−
1
(iv)
√
sec
2
31°
−
1
sec
31°
(v)
sec
31°
√
sec
2
31°
−
1
Question
40
40.
Express
cos
28°
in terms of
cosec
28°
(i)
√
cosec
2
28°
−
1
cosec
28°
(ii)
√
cosec
2
28°
−
1
(iii)
1
√
cosec
2
28°
−
1
(iv)
cosec
28°
√
cosec
2
28°
−
1
(v)
1
cosec
28°
Question
41
41.
Express
tan
56°
in terms of
sin
56°
(i)
1
√
1
−
sin
2
56°
(ii)
sin
56°
√
1
−
sin
2
56°
(iii)
√
1
−
sin
2
56°
sin
56°
(iv)
√
1
−
sin
2
56°
(v)
1
sin
56°
Question
42
42.
Express
tan
70°
in terms of
cos
70°
(i)
√
1
−
cos
2
70°
cos
70°
(ii)
√
1
−
cos
2
70°
(iii)
1
cos
70°
(iv)
cos
70°
√
1
−
cos
2
70°
(v)
1
√
1
−
cos
2
70°
Question
43
43.
Express
tan
24°
in terms of
cot
24°
(i)
1
cot
24°
(ii)
√
1
+
cot
2
24°
(iii)
1
√
1
+
cot
2
24°
(iv)
cot
24°
√
1
+
cot
2
24°
(v)
√
1
+
cot
2
24°
cot
24°
Question
44
44.
Express
tan
43°
in terms of
sec
43°
(i)
1
sec
43°
(ii)
√
sec
2
43°
−
1
sec
43°
(iii)
1
√
sec
2
43°
−
1
(iv)
sec
43°
√
sec
2
43°
−
1
(v)
√
sec
2
43°
−
1
Question
45
45.
Express
tan
70°
in terms of
cosec
70°
(i)
1
cosec
70°
(ii)
√
cosec
2
70°
−
1
(iii)
1
√
cosec
2
70°
−
1
(iv)
√
cosec
2
70°
−
1
cosec
70°
(v)
cosec
70°
√
cosec
2
70°
−
1
Question
46
46.
Express
cot
58°
in terms of
sin
58°
(i)
√
1
−
sin
2
58°
sin
58°
(ii)
√
1
−
sin
2
58°
(iii)
sin
58°
√
1
−
sin
2
58°
(iv)
1
sin
58°
(v)
1
√
1
−
sin
2
58°
Question
47
47.
Express
cot
66°
in terms of
cos
66°
(i)
cos
66°
√
1
−
cos
2
66°
(ii)
√
1
−
cos
2
66°
cos
66°
(iii)
1
√
1
−
cos
2
66°
(iv)
√
1
−
cos
2
66°
(v)
1
cos
66°
Question
48
48.
Express
cot
68°
in terms of
tan
68°
(i)
tan
68°
√
1
+
tan
2
68°
(ii)
1
√
1
+
tan
2
68°
(iii)
√
1
+
tan
2
68°
(iv)
√
1
+
tan
2
68°
tan
68°
(v)
1
tan
68°
Question
49
49.
Express
cot
24°
in terms of
sec
24°
(i)
1
sec
24°
(ii)
√
sec
2
24°
−
1
(iii)
√
sec
2
24°
−
1
sec
24°
(iv)
sec
24°
√
sec
2
24°
−
1
(v)
1
√
sec
2
24°
−
1
Question
50
50.
Express
cot
64°
in terms of
cosec
64°
(i)
√
cosec
2
64°
−
1
cosec
64°
(ii)
√
cosec
2
64°
−
1
(iii)
1
√
cosec
2
64°
−
1
(iv)
cosec
64°
√
cosec
2
64°
−
1
(v)
1
cosec
64°
Question
51
51.
Express
sec
61°
in terms of
sin
61°
(i)
1
√
1
−
sin
2
61°
(ii)
√
1
−
sin
2
61°
sin
61°
(iii)
sin
61°
√
1
−
sin
2
61°
(iv)
1
sin
61°
(v)
√
1
−
sin
2
61°
Question
52
52.
Express
sec
34°
in terms of
cos
34°
(i)
cos
34°
√
1
−
cos
2
34°
(ii)
√
1
−
cos
2
34°
cos
34°
(iii)
√
1
−
cos
2
34°
(iv)
1
√
1
−
cos
2
34°
(v)
1
cos
34°
Question
53
53.
Express
sec
35°
in terms of
tan
35°
(i)
√
1
+
tan
2
35°
(ii)
tan
35°
√
1
+
tan
2
35°
(iii)
1
√
1
+
tan
2
35°
(iv)
1
tan
35°
(v)
√
1
+
tan
2
35°
tan
35°
Question
54
54.
Express
sec
61°
in terms of
cot
61°
(i)
√
1
+
cot
2
61°
(ii)
1
√
1
+
cot
2
61°
(iii)
√
1
+
cot
2
61°
cot
61°
(iv)
1
cot
61°
(v)
cot
61°
√
1
+
cot
2
61°
Question
55
55.
Express
sec
21°
in terms of
cosec
21°
(i)
√
cosec
2
21°
−
1
(ii)
cosec
21°
√
cosec
2
21°
−
1
(iii)
1
cosec
21°
(iv)
1
√
cosec
2
21°
−
1
(v)
√
cosec
2
21°
−
1
cosec
21°
Question
56
56.
Express
cosec
40°
in terms of
sin
40°
(i)
√
1
−
sin
2
40°
(ii)
√
1
−
sin
2
40°
sin
40°
(iii)
1
sin
40°
(iv)
1
√
1
−
sin
2
40°
(v)
sin
40°
√
1
−
sin
2
40°
Question
57
57.
Express
cosec
39°
in terms of
cos
39°
(i)
√
1
−
cos
2
39°
cos
39°
(ii)
1
√
1
−
cos
2
39°
(iii)
cos
39°
√
1
−
cos
2
39°
(iv)
√
1
−
cos
2
39°
(v)
1
cos
39°
Question
58
58.
Express
cosec
72°
in terms of
tan
72°
(i)
√
1
+
tan
2
72°
tan
72°
(ii)
1
√
1
+
tan
2
72°
(iii)
√
1
+
tan
2
72°
(iv)
1
tan
72°
(v)
tan
72°
√
1
+
tan
2
72°
Question
59
59.
Express
cosec
46°
in terms of
cot
46°
(i)
1
√
1
+
cot
2
46°
(ii)
cot
46°
√
1
+
cot
2
46°
(iii)
1
cot
46°
(iv)
√
1
+
cot
2
46°
cot
46°
(v)
√
1
+
cot
2
46°
Question
60
60.
Express
cosec
73°
in terms of
sec
73°
(i)
1
√
sec
2
73°
−
1
(ii)
sec
73°
√
sec
2
73°
−
1
(iii)
√
sec
2
73°
−
1
sec
73°
(iv)
1
sec
73°
(v)
√
sec
2
73°
−
1
Assignment Key
1) (i)
2) (iv)
3) (iv)
4) (i)
5) (i)
6) (iii)
7) (iii)
8) (v)
9) (iv)
10) (v)
11) (iv)
12) (iv)
13) (i)
14) (iv)
15) (iii)
16) (iii)
17) (ii)
18) (v)
19) (v)
20) (v)
21) (iv)
22) (v)
23) (iii)
24) (i)
25) (v)
26) (i)
27) (iv)
28) (iii)
29) (v)
30) (iv)
31) (v)
32) (iii)
33) (iv)
34) (iii)
35) (iv)
36) (v)
37) (v)
38) (ii)
39) (i)
40) (i)
41) (ii)
42) (i)
43) (i)
44) (v)
45) (iii)
46) (i)
47) (i)
48) (v)
49) (v)
50) (ii)
51) (i)
52) (v)
53) (i)
54) (iii)
55) (ii)
56) (iii)
57) (ii)
58) (i)
59) (v)
60) (ii)
