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)
cos
θ
√
1
−
cos
2
θ
(iii)
1
cos
θ
(iv)
√
1
−
cos
2
θ
(v)
1
√
1
−
cos
2
θ
Question
2
2.
Express
sin
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
3
3.
Express
sin
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
4
4.
Express
sin
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
√
sec
2
θ
−
1
sec
θ
(iii)
√
sec
2
θ
−
1
(iv)
1
√
sec
2
θ
−
1
(v)
1
sec
θ
Question
5
5.
Express
sin
θ
in terms of
cosec
θ
(i)
1
√
cosec
2
θ
−
1
(ii)
1
cosec
θ
(iii)
cosec
θ
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
cosec
θ
(v)
√
cosec
2
θ
−
1
Question
6
6.
Express
cos
θ
in terms of
sin
θ
(i)
1
sin
θ
(ii)
1
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
(iv)
√
1
−
sin
2
θ
sin
θ
(v)
sin
θ
√
1
−
sin
2
θ
Question
7
7.
Express
cos
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
1
tan
θ
(iv)
1
√
1
+
tan
2
θ
(v)
tan
θ
√
1
+
tan
2
θ
Question
8
8.
Express
cos
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
+
cot
2
θ
(v)
1
√
1
+
cot
2
θ
Question
9
9.
Express
cos
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
sec
θ
(ii)
sec
θ
√
sec
2
θ
−
1
(iii)
1
sec
θ
(iv)
1
√
sec
2
θ
−
1
(v)
√
sec
2
θ
−
1
Question
10
10.
Express
cos
θ
in terms of
cosec
θ
(i)
1
√
cosec
2
θ
−
1
(ii)
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
cosec
θ
(iv)
1
cosec
θ
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
11
11.
Express
tan
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
sin
θ
(ii)
sin
θ
√
1
−
sin
2
θ
(iii)
1
√
1
−
sin
2
θ
(iv)
1
sin
θ
(v)
√
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
√
1
+
cot
2
θ
(ii)
√
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
(ii)
1
√
sec
2
θ
−
1
(iii)
√
sec
2
θ
−
1
sec
θ
(iv)
sec
θ
√
sec
2
θ
−
1
(v)
1
sec
θ
Question
15
15.
Express
tan
θ
in terms of
cosec
θ
(i)
1
√
cosec
2
θ
−
1
(ii)
1
cosec
θ
(iii)
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
cosec
θ
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
16
16.
Express
cot
θ
in terms of
sin
θ
(i)
1
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
sin
θ
(iii)
1
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
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
1
√
1
−
cos
2
θ
(v)
1
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
tan
θ
(iii)
1
√
1
+
tan
2
θ
(iv)
1
tan
θ
(v)
√
1
+
tan
2
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)
sec
θ
√
sec
2
θ
−
1
(iv)
1
sec
θ
(v)
1
√
sec
2
θ
−
1
Question
20
20.
Express
cot
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
(ii)
cosec
θ
√
cosec
2
θ
−
1
(iii)
1
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
cosec
θ
(v)
1
cosec
θ
Question
21
21.
Express
sec
θ
in terms of
sin
θ
(i)
sin
θ
√
1
−
sin
2
θ
(ii)
1
sin
θ
(iii)
1
√
1
−
sin
2
θ
(iv)
√
1
−
sin
2
θ
(v)
√
1
−
sin
2
θ
sin
θ
Question
22
22.
Express
sec
θ
in terms of
cos
θ
(i)
1
cos
θ
(ii)
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
cos
θ
(iv)
cos
θ
√
1
−
cos
2
θ
(v)
1
√
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
(iii)
1
tan
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
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
cot
θ
(iv)
√
1
+
cot
2
θ
(v)
cot
θ
√
1
+
cot
2
θ
Question
25
25.
Express
sec
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
cosec
θ
(ii)
1
√
cosec
2
θ
−
1
(iii)
1
cosec
θ
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
√
cosec
2
θ
−
1
Question
26
26.
Express
cosec
θ
in terms of
sin
θ
(i)
1
sin
θ
(ii)
√
1
−
sin
2
θ
sin
θ
(iii)
√
1
−
sin
2
θ
(iv)
sin
θ
√
1
−
sin
2
θ
(v)
1
√
1
−
sin
2
θ
Question
27
27.
Express
cosec
θ
in terms of
cos
θ
(i)
cos
θ
√
1
−
cos
2
θ
(ii)
1
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
cos
θ
(v)
1
cos
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
(iv)
1
tan
θ
(v)
√
1
+
tan
2
θ
tan
θ
Question
29
29.
Express
cosec
θ
in terms of
cot
θ
(i)
1
√
1
+
cot
2
θ
(ii)
1
cot
θ
(iii)
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
cot
θ
(v)
cot
θ
√
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)
sec
θ
√
sec
2
θ
−
1
(iv)
√
sec
2
θ
−
1
sec
θ
(v)
1
√
sec
2
θ
−
1
Question
31
31.
Express
sin
61°
in terms of
cos
61°
(i)
√
1
−
cos
2
61°
(ii)
√
1
−
cos
2
61°
cos
61°
(iii)
1
√
1
−
cos
2
61°
(iv)
1
cos
61°
(v)
cos
61°
√
1
−
cos
2
61°
Question
32
32.
Express
sin
51°
in terms of
tan
51°
(i)
tan
51°
√
1
+
tan
2
51°
(ii)
1
√
1
+
tan
2
51°
(iii)
√
1
+
tan
2
51°
tan
51°
(iv)
√
1
+
tan
2
51°
(v)
1
tan
51°
Question
33
33.
Express
sin
50°
in terms of
cot
50°
(i)
√
1
+
cot
2
50°
(ii)
1
√
1
+
cot
2
50°
(iii)
cot
50°
√
1
+
cot
2
50°
(iv)
√
1
+
cot
2
50°
cot
50°
(v)
1
cot
50°
Question
34
34.
Express
sin
20°
in terms of
sec
20°
(i)
1
sec
20°
(ii)
√
sec
2
20°
−
1
sec
20°
(iii)
√
sec
2
20°
−
1
(iv)
1
√
sec
2
20°
−
1
(v)
sec
20°
√
sec
2
20°
−
1
Question
35
35.
Express
sin
36°
in terms of
cosec
36°
(i)
1
cosec
36°
(ii)
√
cosec
2
36°
−
1
cosec
36°
(iii)
√
cosec
2
36°
−
1
(iv)
1
√
cosec
2
36°
−
1
(v)
cosec
36°
√
cosec
2
36°
−
1
Question
36
36.
Express
cos
44°
in terms of
sin
44°
(i)
1
√
1
−
sin
2
44°
(ii)
√
1
−
sin
2
44°
(iii)
sin
44°
√
1
−
sin
2
44°
(iv)
1
sin
44°
(v)
√
1
−
sin
2
44°
sin
44°
Question
37
37.
Express
cos
41°
in terms of
tan
41°
(i)
√
1
+
tan
2
41°
(ii)
tan
41°
√
1
+
tan
2
41°
(iii)
1
√
1
+
tan
2
41°
(iv)
√
1
+
tan
2
41°
tan
41°
(v)
1
tan
41°
Question
38
38.
Express
cos
58°
in terms of
cot
58°
(i)
√
1
+
cot
2
58°
cot
58°
(ii)
1
√
1
+
cot
2
58°
(iii)
√
1
+
cot
2
58°
(iv)
cot
58°
√
1
+
cot
2
58°
(v)
1
cot
58°
Question
39
39.
Express
cos
40°
in terms of
sec
40°
(i)
√
sec
2
40°
−
1
(ii)
1
√
sec
2
40°
−
1
(iii)
√
sec
2
40°
−
1
sec
40°
(iv)
sec
40°
√
sec
2
40°
−
1
(v)
1
sec
40°
Question
40
40.
Express
cos
58°
in terms of
cosec
58°
(i)
√
cosec
2
58°
−
1
(ii)
cosec
58°
√
cosec
2
58°
−
1
(iii)
√
cosec
2
58°
−
1
cosec
58°
(iv)
1
√
cosec
2
58°
−
1
(v)
1
cosec
58°
Question
41
41.
Express
tan
47°
in terms of
sin
47°
(i)
1
sin
47°
(ii)
1
√
1
−
sin
2
47°
(iii)
√
1
−
sin
2
47°
(iv)
√
1
−
sin
2
47°
sin
47°
(v)
sin
47°
√
1
−
sin
2
47°
Question
42
42.
Express
tan
58°
in terms of
cos
58°
(i)
1
√
1
−
cos
2
58°
(ii)
cos
58°
√
1
−
cos
2
58°
(iii)
1
cos
58°
(iv)
√
1
−
cos
2
58°
(v)
√
1
−
cos
2
58°
cos
58°
Question
43
43.
Express
tan
47°
in terms of
cot
47°
(i)
√
1
+
cot
2
47°
cot
47°
(ii)
cot
47°
√
1
+
cot
2
47°
(iii)
1
cot
47°
(iv)
√
1
+
cot
2
47°
(v)
1
√
1
+
cot
2
47°
Question
44
44.
Express
tan
37°
in terms of
sec
37°
(i)
sec
37°
√
sec
2
37°
−
1
(ii)
√
sec
2
37°
−
1
(iii)
1
sec
37°
(iv)
√
sec
2
37°
−
1
sec
37°
(v)
1
√
sec
2
37°
−
1
Question
45
45.
Express
tan
77°
in terms of
cosec
77°
(i)
cosec
77°
√
cosec
2
77°
−
1
(ii)
√
cosec
2
77°
−
1
cosec
77°
(iii)
1
cosec
77°
(iv)
1
√
cosec
2
77°
−
1
(v)
√
cosec
2
77°
−
1
Question
46
46.
Express
cot
79°
in terms of
sin
79°
(i)
1
√
1
−
sin
2
79°
(ii)
1
sin
79°
(iii)
sin
79°
√
1
−
sin
2
79°
(iv)
√
1
−
sin
2
79°
sin
79°
(v)
√
1
−
sin
2
79°
Question
47
47.
Express
cot
64°
in terms of
cos
64°
(i)
1
√
1
−
cos
2
64°
(ii)
√
1
−
cos
2
64°
cos
64°
(iii)
1
cos
64°
(iv)
√
1
−
cos
2
64°
(v)
cos
64°
√
1
−
cos
2
64°
Question
48
48.
Express
cot
47°
in terms of
tan
47°
(i)
1
tan
47°
(ii)
√
1
+
tan
2
47°
tan
47°
(iii)
1
√
1
+
tan
2
47°
(iv)
tan
47°
√
1
+
tan
2
47°
(v)
√
1
+
tan
2
47°
Question
49
49.
Express
cot
72°
in terms of
sec
72°
(i)
1
√
sec
2
72°
−
1
(ii)
1
sec
72°
(iii)
sec
72°
√
sec
2
72°
−
1
(iv)
√
sec
2
72°
−
1
(v)
√
sec
2
72°
−
1
sec
72°
Question
50
50.
Express
cot
27°
in terms of
cosec
27°
(i)
√
cosec
2
27°
−
1
(ii)
1
cosec
27°
(iii)
cosec
27°
√
cosec
2
27°
−
1
(iv)
1
√
cosec
2
27°
−
1
(v)
√
cosec
2
27°
−
1
cosec
27°
Question
51
51.
Express
sec
47°
in terms of
sin
47°
(i)
1
√
1
−
sin
2
47°
(ii)
sin
47°
√
1
−
sin
2
47°
(iii)
√
1
−
sin
2
47°
(iv)
1
sin
47°
(v)
√
1
−
sin
2
47°
sin
47°
Question
52
52.
Express
sec
27°
in terms of
cos
27°
(i)
√
1
−
cos
2
27°
cos
27°
(ii)
cos
27°
√
1
−
cos
2
27°
(iii)
1
√
1
−
cos
2
27°
(iv)
1
cos
27°
(v)
√
1
−
cos
2
27°
Question
53
53.
Express
sec
52°
in terms of
tan
52°
(i)
√
1
+
tan
2
52°
(ii)
√
1
+
tan
2
52°
tan
52°
(iii)
1
tan
52°
(iv)
tan
52°
√
1
+
tan
2
52°
(v)
1
√
1
+
tan
2
52°
Question
54
54.
Express
sec
29°
in terms of
cot
29°
(i)
√
1
+
cot
2
29°
cot
29°
(ii)
1
√
1
+
cot
2
29°
(iii)
√
1
+
cot
2
29°
(iv)
cot
29°
√
1
+
cot
2
29°
(v)
1
cot
29°
Question
55
55.
Express
sec
36°
in terms of
cosec
36°
(i)
cosec
36°
√
cosec
2
36°
−
1
(ii)
√
cosec
2
36°
−
1
(iii)
1
cosec
36°
(iv)
1
√
cosec
2
36°
−
1
(v)
√
cosec
2
36°
−
1
cosec
36°
Question
56
56.
Express
cosec
58°
in terms of
sin
58°
(i)
sin
58°
√
1
−
sin
2
58°
(ii)
1
sin
58°
(iii)
√
1
−
sin
2
58°
sin
58°
(iv)
1
√
1
−
sin
2
58°
(v)
√
1
−
sin
2
58°
Question
57
57.
Express
cosec
39°
in terms of
cos
39°
(i)
cos
39°
√
1
−
cos
2
39°
(ii)
1
cos
39°
(iii)
1
√
1
−
cos
2
39°
(iv)
√
1
−
cos
2
39°
cos
39°
(v)
√
1
−
cos
2
39°
Question
58
58.
Express
cosec
74°
in terms of
tan
74°
(i)
√
1
+
tan
2
74°
tan
74°
(ii)
1
tan
74°
(iii)
1
√
1
+
tan
2
74°
(iv)
tan
74°
√
1
+
tan
2
74°
(v)
√
1
+
tan
2
74°
Question
59
59.
Express
cosec
77°
in terms of
cot
77°
(i)
√
1
+
cot
2
77°
(ii)
1
√
1
+
cot
2
77°
(iii)
1
cot
77°
(iv)
cot
77°
√
1
+
cot
2
77°
(v)
√
1
+
cot
2
77°
cot
77°
Question
60
60.
Express
cosec
76°
in terms of
sec
76°
(i)
1
sec
76°
(ii)
sec
76°
√
sec
2
76°
−
1
(iii)
√
sec
2
76°
−
1
sec
76°
(iv)
√
sec
2
76°
−
1
(v)
1
√
sec
2
76°
−
1
Assignment Key
1) (iv)
2) (iv)
3) (iii)
4) (ii)
5) (ii)
6) (iii)
7) (iv)
8) (i)
9) (iii)
10) (iii)
11) (ii)
12) (iii)
13) (iii)
14) (i)
15) (i)
16) (ii)
17) (iii)
18) (iv)
19) (v)
20) (i)
21) (iii)
22) (i)
23) (ii)
24) (iii)
25) (iv)
26) (i)
27) (ii)
28) (v)
29) (iii)
30) (iii)
31) (i)
32) (i)
33) (ii)
34) (ii)
35) (i)
36) (ii)
37) (iii)
38) (iv)
39) (v)
40) (iii)
41) (v)
42) (v)
43) (iii)
44) (ii)
45) (iv)
46) (iv)
47) (v)
48) (i)
49) (i)
50) (i)
51) (i)
52) (iv)
53) (i)
54) (i)
55) (i)
56) (ii)
57) (iii)
58) (i)
59) (i)
60) (ii)
