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
√
1
−
cos
2
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
(v)
1
cos
θ
Question
2
2.
Express
sin
θ
in terms of
tan
θ
(i)
1
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
(iii)
1
tan
θ
(iv)
√
1
+
tan
2
θ
tan
θ
(v)
tan
θ
√
1
+
tan
2
θ
Question
3
3.
Express
sin
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
4
4.
Express
sin
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
√
sec
2
θ
−
1
(iii)
1
sec
θ
(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)
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
cosec
θ
(iii)
1
√
cosec
2
θ
−
1
(iv)
√
cosec
2
θ
−
1
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
6
6.
Express
cos
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
(ii)
1
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
sin
θ
√
1
−
sin
2
θ
(v)
1
sin
θ
Question
7
7.
Express
cos
θ
in terms of
tan
θ
(i)
tan
θ
√
1
+
tan
2
θ
(ii)
√
1
+
tan
2
θ
tan
θ
(iii)
1
tan
θ
(iv)
1
√
1
+
tan
2
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
cot
θ
(iv)
cot
θ
√
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
(ii)
sec
θ
√
sec
2
θ
−
1
(iii)
1
sec
θ
(iv)
√
sec
2
θ
−
1
sec
θ
(v)
1
√
sec
2
θ
−
1
Question
10
10.
Express
cos
θ
in terms of
cosec
θ
(i)
1
cosec
θ
(ii)
√
cosec
2
θ
−
1
cosec
θ
(iii)
√
cosec
2
θ
−
1
(iv)
1
√
cosec
2
θ
−
1
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
11
11.
Express
tan
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
(ii)
sin
θ
√
1
−
sin
2
θ
(iii)
1
√
1
−
sin
2
θ
(iv)
√
1
−
sin
2
θ
sin
θ
(v)
1
sin
θ
Question
12
12.
Express
tan
θ
in terms of
cos
θ
(i)
1
cos
θ
(ii)
cos
θ
√
1
−
cos
2
θ
(iii)
√
1
−
cos
2
θ
(iv)
1
√
1
−
cos
2
θ
(v)
√
1
−
cos
2
θ
cos
θ
Question
13
13.
Express
tan
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
14
14.
Express
tan
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
15
15.
Express
tan
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
(ii)
√
cosec
2
θ
−
1
cosec
θ
(iii)
1
cosec
θ
(iv)
cosec
θ
√
cosec
2
θ
−
1
(v)
1
√
cosec
2
θ
−
1
Question
16
16.
Express
cot
θ
in terms of
sin
θ
(i)
1
sin
θ
(ii)
√
1
−
sin
2
θ
(iii)
√
1
−
sin
2
θ
sin
θ
(iv)
1
√
1
−
sin
2
θ
(v)
sin
θ
√
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
2
θ
cos
θ
(iv)
√
1
−
cos
2
θ
(v)
1
cos
θ
Question
18
18.
Express
cot
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
19
19.
Express
cot
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
20
20.
Express
cot
θ
in terms of
cosec
θ
(i)
√
cosec
2
θ
−
1
cosec
θ
(ii)
1
√
cosec
2
θ
−
1
(iii)
√
cosec
2
θ
−
1
(iv)
1
cosec
θ
(v)
cosec
θ
√
cosec
2
θ
−
1
Question
21
21.
Express
sec
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
22
22.
Express
sec
θ
in terms of
cos
θ
(i)
1
cos
θ
(ii)
√
1
−
cos
2
θ
cos
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
1
√
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
tan
θ
(v)
√
1
+
tan
2
θ
Question
24
24.
Express
sec
θ
in terms of
cot
θ
(i)
√
1
+
cot
2
θ
(ii)
1
√
1
+
cot
2
θ
(iii)
√
1
+
cot
2
θ
cot
θ
(iv)
1
cot
θ
(v)
cot
θ
√
1
+
cot
2
θ
Question
25
25.
Express
sec
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
26
26.
Express
cosec
θ
in terms of
sin
θ
(i)
√
1
−
sin
2
θ
(ii)
1
sin
θ
(iii)
sin
θ
√
1
−
sin
2
θ
(iv)
1
√
1
−
sin
2
θ
(v)
√
1
−
sin
2
θ
sin
θ
Question
27
27.
Express
cosec
θ
in terms of
cos
θ
(i)
1
cos
θ
(ii)
1
√
1
−
cos
2
θ
(iii)
cos
θ
√
1
−
cos
2
θ
(iv)
√
1
−
cos
2
θ
(v)
√
1
−
cos
2
θ
cos
θ
Question
28
28.
Express
cosec
θ
in terms of
tan
θ
(i)
tan
θ
√
1
+
tan
2
θ
(ii)
1
tan
θ
(iii)
1
√
1
+
tan
2
θ
(iv)
√
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)
1
√
1
+
cot
2
θ
(iii)
cot
θ
√
1
+
cot
2
θ
(iv)
√
1
+
cot
2
θ
(v)
√
1
+
cot
2
θ
cot
θ
Question
30
30.
Express
cosec
θ
in terms of
sec
θ
(i)
sec
θ
√
sec
2
θ
−
1
(ii)
1
√
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
79°
in terms of
cos
79°
(i)
√
1
−
cos
2
79°
cos
79°
(ii)
1
cos
79°
(iii)
√
1
−
cos
2
79°
(iv)
1
√
1
−
cos
2
79°
(v)
cos
79°
√
1
−
cos
2
79°
Question
32
32.
Express
sin
21°
in terms of
tan
21°
(i)
1
√
1
+
tan
2
21°
(ii)
1
tan
21°
(iii)
√
1
+
tan
2
21°
tan
21°
(iv)
√
1
+
tan
2
21°
(v)
tan
21°
√
1
+
tan
2
21°
Question
33
33.
Express
sin
72°
in terms of
cot
72°
(i)
√
1
+
cot
2
72°
(ii)
1
cot
72°
(iii)
√
1
+
cot
2
72°
cot
72°
(iv)
1
√
1
+
cot
2
72°
(v)
cot
72°
√
1
+
cot
2
72°
Question
34
34.
Express
sin
34°
in terms of
sec
34°
(i)
1
sec
34°
(ii)
1
√
sec
2
34°
−
1
(iii)
sec
34°
√
sec
2
34°
−
1
(iv)
√
sec
2
34°
−
1
sec
34°
(v)
√
sec
2
34°
−
1
Question
35
35.
Express
sin
57°
in terms of
cosec
57°
(i)
1
cosec
57°
(ii)
1
√
cosec
2
57°
−
1
(iii)
√
cosec
2
57°
−
1
cosec
57°
(iv)
cosec
57°
√
cosec
2
57°
−
1
(v)
√
cosec
2
57°
−
1
Question
36
36.
Express
cos
60°
in terms of
sin
60°
(i)
√
1
−
sin
2
60°
(ii)
√
1
−
sin
2
60°
sin
60°
(iii)
1
√
1
−
sin
2
60°
(iv)
1
sin
60°
(v)
sin
60°
√
1
−
sin
2
60°
Question
37
37.
Express
cos
56°
in terms of
tan
56°
(i)
1
tan
56°
(ii)
1
√
1
+
tan
2
56°
(iii)
tan
56°
√
1
+
tan
2
56°
(iv)
√
1
+
tan
2
56°
tan
56°
(v)
√
1
+
tan
2
56°
Question
38
38.
Express
cos
58°
in terms of
cot
58°
(i)
cot
58°
√
1
+
cot
2
58°
(ii)
√
1
+
cot
2
58°
(iii)
1
√
1
+
cot
2
58°
(iv)
1
cot
58°
(v)
√
1
+
cot
2
58°
cot
58°
Question
39
39.
Express
cos
24°
in terms of
sec
24°
(i)
√
sec
2
24°
−
1
(ii)
1
√
sec
2
24°
−
1
(iii)
√
sec
2
24°
−
1
sec
24°
(iv)
sec
24°
√
sec
2
24°
−
1
(v)
1
sec
24°
Question
40
40.
Express
cos
53°
in terms of
cosec
53°
(i)
1
cosec
53°
(ii)
1
√
cosec
2
53°
−
1
(iii)
√
cosec
2
53°
−
1
(iv)
cosec
53°
√
cosec
2
53°
−
1
(v)
√
cosec
2
53°
−
1
cosec
53°
Question
41
41.
Express
tan
33°
in terms of
sin
33°
(i)
√
1
−
sin
2
33°
(ii)
sin
33°
√
1
−
sin
2
33°
(iii)
1
sin
33°
(iv)
√
1
−
sin
2
33°
sin
33°
(v)
1
√
1
−
sin
2
33°
Question
42
42.
Express
tan
39°
in terms of
cos
39°
(i)
√
1
−
cos
2
39°
(ii)
√
1
−
cos
2
39°
cos
39°
(iii)
1
cos
39°
(iv)
cos
39°
√
1
−
cos
2
39°
(v)
1
√
1
−
cos
2
39°
Question
43
43.
Express
tan
38°
in terms of
cot
38°
(i)
√
1
+
cot
2
38°
(ii)
cot
38°
√
1
+
cot
2
38°
(iii)
1
√
1
+
cot
2
38°
(iv)
1
cot
38°
(v)
√
1
+
cot
2
38°
cot
38°
Question
44
44.
Express
tan
75°
in terms of
sec
75°
(i)
sec
75°
√
sec
2
75°
−
1
(ii)
1
√
sec
2
75°
−
1
(iii)
√
sec
2
75°
−
1
(iv)
1
sec
75°
(v)
√
sec
2
75°
−
1
sec
75°
Question
45
45.
Express
tan
50°
in terms of
cosec
50°
(i)
1
cosec
50°
(ii)
1
√
cosec
2
50°
−
1
(iii)
√
cosec
2
50°
−
1
cosec
50°
(iv)
cosec
50°
√
cosec
2
50°
−
1
(v)
√
cosec
2
50°
−
1
Question
46
46.
Express
cot
70°
in terms of
sin
70°
(i)
√
1
−
sin
2
70°
sin
70°
(ii)
1
√
1
−
sin
2
70°
(iii)
sin
70°
√
1
−
sin
2
70°
(iv)
1
sin
70°
(v)
√
1
−
sin
2
70°
Question
47
47.
Express
cot
63°
in terms of
cos
63°
(i)
√
1
−
cos
2
63°
cos
63°
(ii)
cos
63°
√
1
−
cos
2
63°
(iii)
1
cos
63°
(iv)
√
1
−
cos
2
63°
(v)
1
√
1
−
cos
2
63°
Question
48
48.
Express
cot
41°
in terms of
tan
41°
(i)
√
1
+
tan
2
41°
tan
41°
(ii)
√
1
+
tan
2
41°
(iii)
tan
41°
√
1
+
tan
2
41°
(iv)
1
√
1
+
tan
2
41°
(v)
1
tan
41°
Question
49
49.
Express
cot
41°
in terms of
sec
41°
(i)
1
sec
41°
(ii)
√
sec
2
41°
−
1
sec
41°
(iii)
√
sec
2
41°
−
1
(iv)
1
√
sec
2
41°
−
1
(v)
sec
41°
√
sec
2
41°
−
1
Question
50
50.
Express
cot
41°
in terms of
cosec
41°
(i)
√
cosec
2
41°
−
1
cosec
41°
(ii)
1
√
cosec
2
41°
−
1
(iii)
1
cosec
41°
(iv)
cosec
41°
√
cosec
2
41°
−
1
(v)
√
cosec
2
41°
−
1
Question
51
51.
Express
sec
75°
in terms of
sin
75°
(i)
1
√
1
−
sin
2
75°
(ii)
sin
75°
√
1
−
sin
2
75°
(iii)
√
1
−
sin
2
75°
(iv)
√
1
−
sin
2
75°
sin
75°
(v)
1
sin
75°
Question
52
52.
Express
sec
78°
in terms of
cos
78°
(i)
cos
78°
√
1
−
cos
2
78°
(ii)
1
cos
78°
(iii)
√
1
−
cos
2
78°
(iv)
1
√
1
−
cos
2
78°
(v)
√
1
−
cos
2
78°
cos
78°
Question
53
53.
Express
sec
41°
in terms of
tan
41°
(i)
1
tan
41°
(ii)
√
1
+
tan
2
41°
tan
41°
(iii)
tan
41°
√
1
+
tan
2
41°
(iv)
√
1
+
tan
2
41°
(v)
1
√
1
+
tan
2
41°
Question
54
54.
Express
sec
50°
in terms of
cot
50°
(i)
cot
50°
√
1
+
cot
2
50°
(ii)
√
1
+
cot
2
50°
cot
50°
(iii)
√
1
+
cot
2
50°
(iv)
1
cot
50°
(v)
1
√
1
+
cot
2
50°
Question
55
55.
Express
sec
29°
in terms of
cosec
29°
(i)
√
cosec
2
29°
−
1
(ii)
cosec
29°
√
cosec
2
29°
−
1
(iii)
1
√
cosec
2
29°
−
1
(iv)
1
cosec
29°
(v)
√
cosec
2
29°
−
1
cosec
29°
Question
56
56.
Express
cosec
49°
in terms of
sin
49°
(i)
1
√
1
−
sin
2
49°
(ii)
√
1
−
sin
2
49°
sin
49°
(iii)
1
sin
49°
(iv)
sin
49°
√
1
−
sin
2
49°
(v)
√
1
−
sin
2
49°
Question
57
57.
Express
cosec
41°
in terms of
cos
41°
(i)
cos
41°
√
1
−
cos
2
41°
(ii)
1
cos
41°
(iii)
1
√
1
−
cos
2
41°
(iv)
√
1
−
cos
2
41°
cos
41°
(v)
√
1
−
cos
2
41°
Question
58
58.
Express
cosec
49°
in terms of
tan
49°
(i)
1
tan
49°
(ii)
tan
49°
√
1
+
tan
2
49°
(iii)
1
√
1
+
tan
2
49°
(iv)
√
1
+
tan
2
49°
(v)
√
1
+
tan
2
49°
tan
49°
Question
59
59.
Express
cosec
75°
in terms of
cot
75°
(i)
√
1
+
cot
2
75°
(ii)
cot
75°
√
1
+
cot
2
75°
(iii)
1
√
1
+
cot
2
75°
(iv)
√
1
+
cot
2
75°
cot
75°
(v)
1
cot
75°
Question
60
60.
Express
cosec
53°
in terms of
sec
53°
(i)
sec
53°
√
sec
2
53°
−
1
(ii)
1
sec
53°
(iii)
√
sec
2
53°
−
1
sec
53°
(iv)
1
√
sec
2
53°
−
1
(v)
√
sec
2
53°
−
1
Assignment Key
1) (iv)
2) (v)
3) (i)
4) (v)
5) (i)
6) (i)
7) (iv)
8) (iv)
9) (iii)
10) (ii)
11) (ii)
12) (v)
13) (ii)
14) (i)
15) (v)
16) (iii)
17) (ii)
18) (iv)
19) (i)
20) (iii)
21) (v)
22) (i)
23) (v)
24) (iii)
25) (iv)
26) (ii)
27) (ii)
28) (v)
29) (iv)
30) (i)
31) (iii)
32) (v)
33) (iv)
34) (iv)
35) (i)
36) (i)
37) (ii)
38) (i)
39) (v)
40) (v)
41) (ii)
42) (ii)
43) (iv)
44) (iii)
45) (ii)
46) (i)
47) (ii)
48) (v)
49) (iv)
50) (v)
51) (i)
52) (ii)
53) (iv)
54) (ii)
55) (ii)
56) (iii)
57) (iii)
58) (v)
59) (i)
60) (i)
