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)
cos
θ
√
1
−
cos
2
θ
(ii)
1
cos
θ
(iii)
√
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
θ
(ii)
tan
θ
√
1
+
tan
2
θ
(iii)
1
√
1
+
tan
2
θ
(iv)
√
1
+
tan
2
θ
(v)
√
1
+
tan
2
θ
tan
θ
Question
3
3.
Express
sin
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
(ii)
√
1
+
cot
2
θ
cot
θ
(iii)
1
√
1
+
cot
2
θ
(iv)
cot
θ
√
1
+
cot
2
θ
(v)
1
cot
θ
Question
4
4.
Express
sin
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
(ii)
1
sec
θ
(iii)
√
sec
2
θ
−
1
sec
θ
(iv)
1
√
sec
2
θ
−
1
(v)
sec
θ
√
sec
2
θ
−
1
Question
5
5.
Express
sin
θ
in terms of
cosec
θ
(i)
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
(iii)
cosec
θ
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
cosec
θ
(v)
1
√
cosec
2
θ
−
1
Question
6
6.
Express
cos
θ
in terms of
sin
θ
(i)
sin
θ
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
sin
θ
(iii)
√
1
−
sin
2
θ
(iv)
1
√
1
−
sin
2
θ
(v)
1
sin
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
+
tan
2
θ
tan
θ
(iv)
√
1
+
tan
2
θ
(v)
1
√
1
+
tan
2
θ
Question
8
8.
Express
cos
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
(ii)
√
1
+
cot
2
θ
cot
θ
(iii)
1
cot
θ
(iv)
1
√
1
+
cot
2
θ
(v)
cot
θ
√
1
+
cot
2
θ
Question
9
9.
Express
cos
θ
in terms of
sec
θ
(i)
1
√
sec
2
θ
−
1
(ii)
√
sec
2
θ
−
1
sec
θ
(iii)
1
sec
θ
(iv)
√
sec
2
θ
−
1
(v)
sec
θ
√
sec
2
θ
−
1
Question
10
10.
Express
cos
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
(ii)
√
cosec
2
θ
−
1
cosec
θ
(iii)
cosec
θ
√
cosec
2
θ
−
1
(iv)
1
cosec
θ
(v)
1
√
cosec
2
θ
−
1
Question
11
11.
Express
tan
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
sin
θ
(ii)
√
1
−
sin
2
θ
(iii)
1
sin
θ
(iv)
1
√
1
−
sin
2
θ
(v)
sin
θ
√
1
−
sin
2
θ
Question
12
12.
Express
tan
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
cos
θ
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
cos
θ
(iv)
1
cos
θ
(v)
√
1
−
cos
2
θ
Question
13
13.
Express
tan
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
1
cot
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)
√
sec
2
θ
−
1
sec
θ
(ii)
√
sec
2
θ
−
1
(iii)
sec
θ
√
sec
2
θ
−
1
(iv)
1
sec
θ
(v)
1
√
sec
2
θ
−
1
Question
15
15.
Express
tan
θ
in terms of
cosec
θ
(i)
cosec
θ
√
cosec
2
θ
−
1
(ii)
√
cosec
2
θ
−
1
cosec
θ
(iii)
1
cosec
θ
(iv)
√
cosec
2
θ
−
1
(v)
1
√
cosec
2
θ
−
1
Question
16
16.
Express
cot
θ
in terms of
sin
θ
(i)
1
√
1
−
sin
2
θ
(ii)
1
sin
θ
(iii)
sin
θ
√
1
−
sin
2
θ
(iv)
√
1
−
sin
2
θ
sin
θ
(v)
√
1
−
sin
2
θ
Question
17
17.
Express
cot
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
1
cos
θ
(iii)
√
1
−
cos
2
θ
(iv)
cos
θ
√
1
−
cos
2
θ
(v)
√
1
−
cos
2
θ
cos
θ
Question
18
18.
Express
cot
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
(v)
√
1
+
tan
2
θ
tan
θ
Question
19
19.
Express
cot
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
(ii)
1
sec
θ
(iii)
sec
θ
√
sec
2
θ
−
1
(iv)
√
sec
2
θ
−
1
sec
θ
(v)
1
√
sec
2
θ
−
1
Question
20
20.
Express
cot
θ
in terms of
cosec
θ
(i)
cosec
θ
√
cosec
2
θ
−
1
(ii)
1
cosec
θ
(iii)
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
cosec
θ
(v)
1
√
cosec
2
θ
−
1
Question
21
21.
Express
sec
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
sin
θ
(v)
√
1
−
sin
2
θ
Question
22
22.
Express
sec
θ
in terms of
cos
θ
(i)
1
cos
θ
(ii)
1
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
cos
θ
(iv)
cos
θ
√
1
−
cos
2
θ
(v)
√
1
−
cos
2
θ
Question
23
23.
Express
sec
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
(v)
√
1
+
tan
2
θ
tan
θ
Question
24
24.
Express
sec
θ
in terms of
cot
θ
(i)
cot
θ
√
1
+
cot
2
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
cot
θ
(v)
1
cot
θ
Question
25
25.
Express
sec
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
cosec
θ
(ii)
cosec
θ
√
cosec
2
θ
−
1
(iii)
1
cosec
θ
(iv)
√
cosec
2
θ
−
1
(v)
1
√
cosec
2
θ
−
1
Question
26
26.
Express
cosec
θ
in terms of
sin
θ
(i)
sin
θ
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
sin
θ
(iii)
√
1
−
sin
2
θ
(iv)
1
sin
θ
(v)
1
√
1
−
sin
2
θ
Question
27
27.
Express
cosec
θ
in terms of
cos
θ
(i)
1
cos
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
1
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
(v)
cos
θ
√
1
−
cos
2
θ
Question
28
28.
Express
cosec
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
tan
θ
(ii)
1
√
1
+
tan
2
θ
(iii)
1
tan
θ
(iv)
√
1
+
tan
2
θ
(v)
tan
θ
√
1
+
tan
2
θ
Question
29
29.
Express
cosec
θ
in terms of
cot
θ
(i)
1
cot
θ
(ii)
√
1
+
cot
2
θ
cot
θ
(iii)
1
√
1
+
cot
2
θ
(iv)
cot
θ
√
1
+
cot
2
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
2
θ
−
1
sec
θ
(iii)
sec
θ
√
sec
2
θ
−
1
(iv)
1
sec
θ
(v)
√
sec
2
θ
−
1
Question
31
31.
Express
sin
50°
in terms of
cos
50°
(i)
√
1
−
cos
2
50°
(ii)
cos
50°
√
1
−
cos
2
50°
(iii)
√
1
−
cos
2
50°
cos
50°
(iv)
1
cos
50°
(v)
1
√
1
−
cos
2
50°
Question
32
32.
Express
sin
28°
in terms of
tan
28°
(i)
1
tan
28°
(ii)
1
√
1
+
tan
2
28°
(iii)
√
1
+
tan
2
28°
(iv)
√
1
+
tan
2
28°
tan
28°
(v)
tan
28°
√
1
+
tan
2
28°
Question
33
33.
Express
sin
52°
in terms of
cot
52°
(i)
√
1
+
cot
2
52°
(ii)
cot
52°
√
1
+
cot
2
52°
(iii)
1
cot
52°
(iv)
√
1
+
cot
2
52°
cot
52°
(v)
1
√
1
+
cot
2
52°
Question
34
34.
Express
sin
79°
in terms of
sec
79°
(i)
1
sec
79°
(ii)
1
√
sec
2
79°
−
1
(iii)
√
sec
2
79°
−
1
sec
79°
(iv)
sec
79°
√
sec
2
79°
−
1
(v)
√
sec
2
79°
−
1
Question
35
35.
Express
sin
53°
in terms of
cosec
53°
(i)
cosec
53°
√
cosec
2
53°
−
1
(ii)
1
cosec
53°
(iii)
√
cosec
2
53°
−
1
(iv)
√
cosec
2
53°
−
1
cosec
53°
(v)
1
√
cosec
2
53°
−
1
Question
36
36.
Express
cos
68°
in terms of
sin
68°
(i)
√
1
−
sin
2
68°
sin
68°
(ii)
sin
68°
√
1
−
sin
2
68°
(iii)
√
1
−
sin
2
68°
(iv)
1
sin
68°
(v)
1
√
1
−
sin
2
68°
Question
37
37.
Express
cos
20°
in terms of
tan
20°
(i)
tan
20°
√
1
+
tan
2
20°
(ii)
√
1
+
tan
2
20°
(iii)
1
tan
20°
(iv)
1
√
1
+
tan
2
20°
(v)
√
1
+
tan
2
20°
tan
20°
Question
38
38.
Express
cos
28°
in terms of
cot
28°
(i)
1
cot
28°
(ii)
1
√
1
+
cot
2
28°
(iii)
√
1
+
cot
2
28°
(iv)
cot
28°
√
1
+
cot
2
28°
(v)
√
1
+
cot
2
28°
cot
28°
Question
39
39.
Express
cos
38°
in terms of
sec
38°
(i)
1
sec
38°
(ii)
√
sec
2
38°
−
1
(iii)
√
sec
2
38°
−
1
sec
38°
(iv)
sec
38°
√
sec
2
38°
−
1
(v)
1
√
sec
2
38°
−
1
Question
40
40.
Express
cos
34°
in terms of
cosec
34°
(i)
√
cosec
2
34°
−
1
cosec
34°
(ii)
1
√
cosec
2
34°
−
1
(iii)
cosec
34°
√
cosec
2
34°
−
1
(iv)
1
cosec
34°
(v)
√
cosec
2
34°
−
1
Question
41
41.
Express
tan
50°
in terms of
sin
50°
(i)
1
sin
50°
(ii)
√
1
−
sin
2
50°
(iii)
sin
50°
√
1
−
sin
2
50°
(iv)
√
1
−
sin
2
50°
sin
50°
(v)
1
√
1
−
sin
2
50°
Question
42
42.
Express
tan
44°
in terms of
cos
44°
(i)
1
cos
44°
(ii)
cos
44°
√
1
−
cos
2
44°
(iii)
√
1
−
cos
2
44°
cos
44°
(iv)
√
1
−
cos
2
44°
(v)
1
√
1
−
cos
2
44°
Question
43
43.
Express
tan
45°
in terms of
cot
45°
(i)
1
cot
45°
(ii)
√
1
+
cot
2
45°
(iii)
1
√
1
+
cot
2
45°
(iv)
cot
45°
√
1
+
cot
2
45°
(v)
√
1
+
cot
2
45°
cot
45°
Question
44
44.
Express
tan
58°
in terms of
sec
58°
(i)
1
√
sec
2
58°
−
1
(ii)
1
sec
58°
(iii)
sec
58°
√
sec
2
58°
−
1
(iv)
√
sec
2
58°
−
1
(v)
√
sec
2
58°
−
1
sec
58°
Question
45
45.
Express
tan
46°
in terms of
cosec
46°
(i)
1
√
cosec
2
46°
−
1
(ii)
cosec
46°
√
cosec
2
46°
−
1
(iii)
1
cosec
46°
(iv)
√
cosec
2
46°
−
1
(v)
√
cosec
2
46°
−
1
cosec
46°
Question
46
46.
Express
cot
73°
in terms of
sin
73°
(i)
√
1
−
sin
2
73°
sin
73°
(ii)
sin
73°
√
1
−
sin
2
73°
(iii)
√
1
−
sin
2
73°
(iv)
1
sin
73°
(v)
1
√
1
−
sin
2
73°
Question
47
47.
Express
cot
48°
in terms of
cos
48°
(i)
1
√
1
−
cos
2
48°
(ii)
√
1
−
cos
2
48°
cos
48°
(iii)
√
1
−
cos
2
48°
(iv)
cos
48°
√
1
−
cos
2
48°
(v)
1
cos
48°
Question
48
48.
Express
cot
35°
in terms of
tan
35°
(i)
1
tan
35°
(ii)
√
1
+
tan
2
35°
tan
35°
(iii)
√
1
+
tan
2
35°
(iv)
1
√
1
+
tan
2
35°
(v)
tan
35°
√
1
+
tan
2
35°
Question
49
49.
Express
cot
50°
in terms of
sec
50°
(i)
√
sec
2
50°
−
1
(ii)
1
sec
50°
(iii)
sec
50°
√
sec
2
50°
−
1
(iv)
1
√
sec
2
50°
−
1
(v)
√
sec
2
50°
−
1
sec
50°
Question
50
50.
Express
cot
21°
in terms of
cosec
21°
(i)
cosec
21°
√
cosec
2
21°
−
1
(ii)
1
cosec
21°
(iii)
1
√
cosec
2
21°
−
1
(iv)
√
cosec
2
21°
−
1
cosec
21°
(v)
√
cosec
2
21°
−
1
Question
51
51.
Express
sec
38°
in terms of
sin
38°
(i)
sin
38°
√
1
−
sin
2
38°
(ii)
√
1
−
sin
2
38°
(iii)
√
1
−
sin
2
38°
sin
38°
(iv)
1
sin
38°
(v)
1
√
1
−
sin
2
38°
Question
52
52.
Express
sec
65°
in terms of
cos
65°
(i)
1
√
1
−
cos
2
65°
(ii)
√
1
−
cos
2
65°
(iii)
cos
65°
√
1
−
cos
2
65°
(iv)
1
cos
65°
(v)
√
1
−
cos
2
65°
cos
65°
Question
53
53.
Express
sec
78°
in terms of
tan
78°
(i)
√
1
+
tan
2
78°
(ii)
√
1
+
tan
2
78°
tan
78°
(iii)
1
√
1
+
tan
2
78°
(iv)
tan
78°
√
1
+
tan
2
78°
(v)
1
tan
78°
Question
54
54.
Express
sec
79°
in terms of
cot
79°
(i)
cot
79°
√
1
+
cot
2
79°
(ii)
1
√
1
+
cot
2
79°
(iii)
√
1
+
cot
2
79°
(iv)
√
1
+
cot
2
79°
cot
79°
(v)
1
cot
79°
Question
55
55.
Express
sec
46°
in terms of
cosec
46°
(i)
√
cosec
2
46°
−
1
cosec
46°
(ii)
1
cosec
46°
(iii)
cosec
46°
√
cosec
2
46°
−
1
(iv)
√
cosec
2
46°
−
1
(v)
1
√
cosec
2
46°
−
1
Question
56
56.
Express
cosec
73°
in terms of
sin
73°
(i)
1
√
1
−
sin
2
73°
(ii)
1
sin
73°
(iii)
sin
73°
√
1
−
sin
2
73°
(iv)
√
1
−
sin
2
73°
(v)
√
1
−
sin
2
73°
sin
73°
Question
57
57.
Express
cosec
37°
in terms of
cos
37°
(i)
1
√
1
−
cos
2
37°
(ii)
√
1
−
cos
2
37°
(iii)
1
cos
37°
(iv)
cos
37°
√
1
−
cos
2
37°
(v)
√
1
−
cos
2
37°
cos
37°
Question
58
58.
Express
cosec
64°
in terms of
tan
64°
(i)
√
1
+
tan
2
64°
(ii)
tan
64°
√
1
+
tan
2
64°
(iii)
√
1
+
tan
2
64°
tan
64°
(iv)
1
tan
64°
(v)
1
√
1
+
tan
2
64°
Question
59
59.
Express
cosec
23°
in terms of
cot
23°
(i)
1
√
1
+
cot
2
23°
(ii)
√
1
+
cot
2
23°
(iii)
√
1
+
cot
2
23°
cot
23°
(iv)
cot
23°
√
1
+
cot
2
23°
(v)
1
cot
23°
Question
60
60.
Express
cosec
27°
in terms of
sec
27°
(i)
1
sec
27°
(ii)
sec
27°
√
sec
2
27°
−
1
(iii)
√
sec
2
27°
−
1
sec
27°
(iv)
1
√
sec
2
27°
−
1
(v)
√
sec
2
27°
−
1
Assignment Key
1) (iii)
2) (ii)
3) (iii)
4) (iii)
5) (i)
6) (iii)
7) (v)
8) (v)
9) (iii)
10) (ii)
11) (v)
12) (iii)
13) (iii)
14) (ii)
15) (v)
16) (iv)
17) (iv)
18) (i)
19) (v)
20) (iii)
21) (i)
22) (i)
23) (iv)
24) (iv)
25) (ii)
26) (iv)
27) (iii)
28) (i)
29) (v)
30) (iii)
31) (i)
32) (v)
33) (v)
34) (iii)
35) (ii)
36) (iii)
37) (iv)
38) (iv)
39) (i)
40) (i)
41) (iii)
42) (iii)
43) (i)
44) (iv)
45) (i)
46) (i)
47) (iv)
48) (i)
49) (iv)
50) (v)
51) (v)
52) (iv)
53) (i)
54) (iv)
55) (iii)
56) (ii)
57) (i)
58) (iii)
59) (ii)
60) (ii)
