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
−
cos
2
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
1
√
1
−
cos
2
θ
(v)
1
cos
θ
Question
2
2.
Express
sin
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
tan
θ
(ii)
1
√
1
+
tan
2
θ
(iii)
√
1
+
tan
2
θ
(iv)
tan
θ
√
1
+
tan
2
θ
(v)
1
tan
θ
Question
3
3.
Express
sin
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
cot
θ
(ii)
cot
θ
√
1
+
cot
2
θ
(iii)
1
cot
θ
(iv)
√
1
+
cot
2
θ
(v)
1
√
1
+
cot
2
θ
Question
4
4.
Express
sin
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
sec
θ
(ii)
√
sec
2
θ
−
1
(iii)
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)
1
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
cosec
θ
(v)
cosec
θ
√
cosec
2
θ
−
1
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)
sin
θ
√
1
−
sin
2
θ
(iv)
√
1
−
sin
2
θ
(v)
1
sin
θ
Question
7
7.
Express
cos
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
1
√
1
+
tan
2
θ
(iii)
√
1
+
tan
2
θ
tan
θ
(iv)
tan
θ
√
1
+
tan
2
θ
(v)
1
tan
θ
Question
8
8.
Express
cos
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
cot
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
cot
θ
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
(v)
1
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)
1
sec
θ
(v)
sec
θ
√
sec
2
θ
−
1
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
2
θ
−
1
cosec
θ
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
11
11.
Express
tan
θ
in terms of
sin
θ
(i)
sin
θ
√
1
−
sin
2
θ
(ii)
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
1
√
1
−
sin
2
θ
(v)
1
sin
θ
Question
12
12.
Express
tan
θ
in terms of
cos
θ
(i)
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
1
cos
θ
(iv)
1
√
1
−
cos
2
θ
(v)
cos
θ
√
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
cot
θ
(iii)
1
cot
θ
(iv)
√
1
+
cot
2
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
θ
(iii)
√
sec
2
θ
−
1
sec
θ
(iv)
1
√
sec
2
θ
−
1
(v)
sec
θ
√
sec
2
θ
−
1
Question
15
15.
Express
tan
θ
in terms of
cosec
θ
(i)
cosec
θ
√
cosec
2
θ
−
1
(ii)
1
cosec
θ
(iii)
√
cosec
2
θ
−
1
(iv)
1
√
cosec
2
θ
−
1
(v)
√
cosec
2
θ
−
1
cosec
θ
Question
16
16.
Express
cot
θ
in terms of
sin
θ
(i)
1
sin
θ
(ii)
1
√
1
−
sin
2
θ
(iii)
sin
θ
√
1
−
sin
2
θ
(iv)
√
1
−
sin
2
θ
(v)
√
1
−
sin
2
θ
sin
θ
Question
17
17.
Express
cot
θ
in terms of
cos
θ
(i)
√
1
−
cos
2
θ
cos
θ
(ii)
√
1
−
cos
2
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
(iii)
1
√
1
+
tan
2
θ
(iv)
√
1
+
tan
2
θ
tan
θ
(v)
1
tan
θ
Question
19
19.
Express
cot
θ
in terms of
sec
θ
(i)
√
sec
2
θ
−
1
sec
θ
(ii)
√
sec
2
θ
−
1
(iii)
1
sec
θ
(iv)
1
√
sec
2
θ
−
1
(v)
sec
θ
√
sec
2
θ
−
1
Question
20
20.
Express
cot
θ
in terms of
cosec
θ
(i)
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
(iii)
cosec
θ
√
cosec
2
θ
−
1
(iv)
1
√
cosec
2
θ
−
1
(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
θ
(v)
√
1
−
sin
2
θ
Question
22
22.
Express
sec
θ
in terms of
cos
θ
(i)
1
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
cos
θ
(iv)
1
cos
θ
(v)
cos
θ
√
1
−
cos
2
θ
Question
23
23.
Express
sec
θ
in terms of
tan
θ
(i)
√
1
+
tan
2
θ
(ii)
1
√
1
+
tan
2
θ
(iii)
1
tan
θ
(iv)
√
1
+
tan
2
θ
tan
θ
(v)
tan
θ
√
1
+
tan
2
θ
Question
24
24.
Express
sec
θ
in terms of
cot
θ
(i)
cot
θ
√
1
+
cot
2
θ
(ii)
√
1
+
cot
2
θ
(iii)
1
cot
θ
(iv)
1
√
1
+
cot
2
θ
(v)
√
1
+
cot
2
θ
cot
θ
Question
25
25.
Express
sec
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
2
θ
−
1
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
26
26.
Express
cosec
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
sin
θ
(ii)
1
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
(iv)
1
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
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
1
cos
θ
(iv)
1
√
1
−
cos
2
θ
(v)
cos
θ
√
1
−
cos
2
θ
Question
28
28.
Express
cosec
θ
in terms of
tan
θ
(i)
1
√
1
+
tan
2
θ
(ii)
tan
θ
√
1
+
tan
2
θ
(iii)
1
tan
θ
(iv)
√
1
+
tan
2
θ
tan
θ
(v)
√
1
+
tan
2
θ
Question
29
29.
Express
cosec
θ
in terms of
cot
θ
(i)
cot
θ
√
1
+
cot
2
θ
(ii)
√
1
+
cot
2
θ
cot
θ
(iii)
√
1
+
cot
2
θ
(iv)
1
cot
θ
(v)
1
√
1
+
cot
2
θ
Question
30
30.
Express
cosec
θ
in terms of
sec
θ
(i)
1
sec
θ
(ii)
1
√
sec
2
θ
−
1
(iii)
√
sec
2
θ
−
1
(iv)
√
sec
2
θ
−
1
sec
θ
(v)
sec
θ
√
sec
2
θ
−
1
Question
31
31.
Express
sin
35°
in terms of
cos
35°
(i)
1
cos
35°
(ii)
cos
35°
√
1
−
cos
2
35°
(iii)
√
1
−
cos
2
35°
(iv)
1
√
1
−
cos
2
35°
(v)
√
1
−
cos
2
35°
cos
35°
Question
32
32.
Express
sin
70°
in terms of
tan
70°
(i)
1
√
1
+
tan
2
70°
(ii)
1
tan
70°
(iii)
√
1
+
tan
2
70°
tan
70°
(iv)
tan
70°
√
1
+
tan
2
70°
(v)
√
1
+
tan
2
70°
Question
33
33.
Express
sin
29°
in terms of
cot
29°
(i)
cot
29°
√
1
+
cot
2
29°
(ii)
√
1
+
cot
2
29°
(iii)
1
cot
29°
(iv)
√
1
+
cot
2
29°
cot
29°
(v)
1
√
1
+
cot
2
29°
Question
34
34.
Express
sin
37°
in terms of
sec
37°
(i)
1
sec
37°
(ii)
sec
37°
√
sec
2
37°
−
1
(iii)
√
sec
2
37°
−
1
sec
37°
(iv)
1
√
sec
2
37°
−
1
(v)
√
sec
2
37°
−
1
Question
35
35.
Express
sin
73°
in terms of
cosec
73°
(i)
1
√
cosec
2
73°
−
1
(ii)
cosec
73°
√
cosec
2
73°
−
1
(iii)
√
cosec
2
73°
−
1
(iv)
√
cosec
2
73°
−
1
cosec
73°
(v)
1
cosec
73°
Question
36
36.
Express
cos
52°
in terms of
sin
52°
(i)
1
sin
52°
(ii)
√
1
−
sin
2
52°
sin
52°
(iii)
sin
52°
√
1
−
sin
2
52°
(iv)
√
1
−
sin
2
52°
(v)
1
√
1
−
sin
2
52°
Question
37
37.
Express
cos
37°
in terms of
tan
37°
(i)
1
tan
37°
(ii)
√
1
+
tan
2
37°
tan
37°
(iii)
√
1
+
tan
2
37°
(iv)
1
√
1
+
tan
2
37°
(v)
tan
37°
√
1
+
tan
2
37°
Question
38
38.
Express
cos
39°
in terms of
cot
39°
(i)
1
cot
39°
(ii)
√
1
+
cot
2
39°
(iii)
cot
39°
√
1
+
cot
2
39°
(iv)
√
1
+
cot
2
39°
cot
39°
(v)
1
√
1
+
cot
2
39°
Question
39
39.
Express
cos
77°
in terms of
sec
77°
(i)
√
sec
2
77°
−
1
sec
77°
(ii)
√
sec
2
77°
−
1
(iii)
1
√
sec
2
77°
−
1
(iv)
1
sec
77°
(v)
sec
77°
√
sec
2
77°
−
1
Question
40
40.
Express
cos
73°
in terms of
cosec
73°
(i)
cosec
73°
√
cosec
2
73°
−
1
(ii)
√
cosec
2
73°
−
1
(iii)
1
cosec
73°
(iv)
√
cosec
2
73°
−
1
cosec
73°
(v)
1
√
cosec
2
73°
−
1
Question
41
41.
Express
tan
71°
in terms of
sin
71°
(i)
1
√
1
−
sin
2
71°
(ii)
√
1
−
sin
2
71°
sin
71°
(iii)
sin
71°
√
1
−
sin
2
71°
(iv)
√
1
−
sin
2
71°
(v)
1
sin
71°
Question
42
42.
Express
tan
25°
in terms of
cos
25°
(i)
1
cos
25°
(ii)
√
1
−
cos
2
25°
(iii)
1
√
1
−
cos
2
25°
(iv)
√
1
−
cos
2
25°
cos
25°
(v)
cos
25°
√
1
−
cos
2
25°
Question
43
43.
Express
tan
43°
in terms of
cot
43°
(i)
cot
43°
√
1
+
cot
2
43°
(ii)
√
1
+
cot
2
43°
(iii)
√
1
+
cot
2
43°
cot
43°
(iv)
1
cot
43°
(v)
1
√
1
+
cot
2
43°
Question
44
44.
Express
tan
24°
in terms of
sec
24°
(i)
1
sec
24°
(ii)
sec
24°
√
sec
2
24°
−
1
(iii)
1
√
sec
2
24°
−
1
(iv)
√
sec
2
24°
−
1
sec
24°
(v)
√
sec
2
24°
−
1
Question
45
45.
Express
tan
63°
in terms of
cosec
63°
(i)
√
cosec
2
63°
−
1
cosec
63°
(ii)
√
cosec
2
63°
−
1
(iii)
1
√
cosec
2
63°
−
1
(iv)
cosec
63°
√
cosec
2
63°
−
1
(v)
1
cosec
63°
Question
46
46.
Express
cot
62°
in terms of
sin
62°
(i)
1
√
1
−
sin
2
62°
(ii)
sin
62°
√
1
−
sin
2
62°
(iii)
√
1
−
sin
2
62°
(iv)
√
1
−
sin
2
62°
sin
62°
(v)
1
sin
62°
Question
47
47.
Express
cot
77°
in terms of
cos
77°
(i)
√
1
−
cos
2
77°
cos
77°
(ii)
1
cos
77°
(iii)
1
√
1
−
cos
2
77°
(iv)
√
1
−
cos
2
77°
(v)
cos
77°
√
1
−
cos
2
77°
Question
48
48.
Express
cot
23°
in terms of
tan
23°
(i)
√
1
+
tan
2
23°
tan
23°
(ii)
√
1
+
tan
2
23°
(iii)
tan
23°
√
1
+
tan
2
23°
(iv)
1
tan
23°
(v)
1
√
1
+
tan
2
23°
Question
49
49.
Express
cot
71°
in terms of
sec
71°
(i)
√
sec
2
71°
−
1
sec
71°
(ii)
√
sec
2
71°
−
1
(iii)
1
√
sec
2
71°
−
1
(iv)
1
sec
71°
(v)
sec
71°
√
sec
2
71°
−
1
Question
50
50.
Express
cot
25°
in terms of
cosec
25°
(i)
cosec
25°
√
cosec
2
25°
−
1
(ii)
√
cosec
2
25°
−
1
(iii)
1
cosec
25°
(iv)
√
cosec
2
25°
−
1
cosec
25°
(v)
1
√
cosec
2
25°
−
1
Question
51
51.
Express
sec
72°
in terms of
sin
72°
(i)
1
√
1
−
sin
2
72°
(ii)
sin
72°
√
1
−
sin
2
72°
(iii)
1
sin
72°
(iv)
√
1
−
sin
2
72°
sin
72°
(v)
√
1
−
sin
2
72°
Question
52
52.
Express
sec
74°
in terms of
cos
74°
(i)
1
cos
74°
(ii)
√
1
−
cos
2
74°
(iii)
√
1
−
cos
2
74°
cos
74°
(iv)
cos
74°
√
1
−
cos
2
74°
(v)
1
√
1
−
cos
2
74°
Question
53
53.
Express
sec
47°
in terms of
tan
47°
(i)
√
1
+
tan
2
47°
(ii)
√
1
+
tan
2
47°
tan
47°
(iii)
tan
47°
√
1
+
tan
2
47°
(iv)
1
tan
47°
(v)
1
√
1
+
tan
2
47°
Question
54
54.
Express
sec
40°
in terms of
cot
40°
(i)
cot
40°
√
1
+
cot
2
40°
(ii)
√
1
+
cot
2
40°
(iii)
1
cot
40°
(iv)
1
√
1
+
cot
2
40°
(v)
√
1
+
cot
2
40°
cot
40°
Question
55
55.
Express
sec
30°
in terms of
cosec
30°
(i)
√
cosec
2
30°
−
1
cosec
30°
(ii)
cosec
30°
√
cosec
2
30°
−
1
(iii)
√
cosec
2
30°
−
1
(iv)
1
cosec
30°
(v)
1
√
cosec
2
30°
−
1
Question
56
56.
Express
cosec
52°
in terms of
sin
52°
(i)
√
1
−
sin
2
52°
sin
52°
(ii)
sin
52°
√
1
−
sin
2
52°
(iii)
1
√
1
−
sin
2
52°
(iv)
1
sin
52°
(v)
√
1
−
sin
2
52°
Question
57
57.
Express
cosec
64°
in terms of
cos
64°
(i)
cos
64°
√
1
−
cos
2
64°
(ii)
1
cos
64°
(iii)
√
1
−
cos
2
64°
(iv)
√
1
−
cos
2
64°
cos
64°
(v)
1
√
1
−
cos
2
64°
Question
58
58.
Express
cosec
73°
in terms of
tan
73°
(i)
1
√
1
+
tan
2
73°
(ii)
√
1
+
tan
2
73°
(iii)
√
1
+
tan
2
73°
tan
73°
(iv)
1
tan
73°
(v)
tan
73°
√
1
+
tan
2
73°
Question
59
59.
Express
cosec
67°
in terms of
cot
67°
(i)
√
1
+
cot
2
67°
(ii)
1
√
1
+
cot
2
67°
(iii)
cot
67°
√
1
+
cot
2
67°
(iv)
1
cot
67°
(v)
√
1
+
cot
2
67°
cot
67°
Question
60
60.
Express
cosec
48°
in terms of
sec
48°
(i)
sec
48°
√
sec
2
48°
−
1
(ii)
√
sec
2
48°
−
1
(iii)
1
sec
48°
(iv)
√
sec
2
48°
−
1
sec
48°
(v)
1
√
sec
2
48°
−
1
Assignment Key
1) (ii)
2) (iv)
3) (v)
4) (i)
5) (i)
6) (iv)
7) (ii)
8) (iii)
9) (iv)
10) (iv)
11) (i)
12) (ii)
13) (iii)
14) (i)
15) (iv)
16) (v)
17) (iii)
18) (v)
19) (iv)
20) (ii)
21) (ii)
22) (iv)
23) (i)
24) (v)
25) (v)
26) (iv)
27) (iv)
28) (iv)
29) (iii)
30) (v)
31) (iii)
32) (iv)
33) (v)
34) (iii)
35) (v)
36) (iv)
37) (iv)
38) (iii)
39) (iv)
40) (iv)
41) (iii)
42) (iv)
43) (iv)
44) (v)
45) (iii)
46) (iv)
47) (v)
48) (iv)
49) (iii)
50) (ii)
51) (i)
52) (i)
53) (i)
54) (v)
55) (ii)
56) (iv)
57) (v)
58) (iii)
59) (i)
60) (i)
