1) If sinx= 3/5, find the values of other trigonometric ratios.
2) If cosx= 4/5, find the values of other trigonometric ratios.
3) If sinx= 1/√2, find the values of other trigonometric ratios.
4) If cot x= 9/40, find the values of cosec x, sec x. 41/40, 41/9
5) If tanx = 8/15 find sinx. 8/17
6) If sinx = 8/17 find tanx. 8/15
7) If cosx =1/2 find the value of 2sec x/(1+tan²x). 1
8) If tanx = 1/√2 find the value of (cosec²x- sec²x)/(cosec²x+ cot²x) 3/10
9) If 5 tanx = 12 find the value of (2cosx+sinx)/(sinx - cosx). 22/7
10) If 3tanx = 4 find the value of (5sinx-3cosx)/(5sinx+2cosx). 11/26
11) If 3 cot x = 4 find the value of (5cosx - 2sinx)/(5cosx+3sinx). 14/29
12) If tanx = 12/5 find the value of (1+ sin x)/(1- sinx). 25
13) If sinx = 3/5 find the value of (tanx + sec x)². 4
14) If tanx = 3/4 find the value of (1- cosx)/(1+cosx). 1/9
15) If cosx = 3/5 find the value of cot x + cosec x. 2
16) If cosec A= √2 find (2sin²A + 3cot²A)/(4tan²A- cos²A). 8/7
17) If tanx = 12/5 find (1+sinx)/(1- sinx). 25
18) If cot B = 1/√3 find the value of (1- cos²B)/(2- sin²B). 3/5
19) If sec x = 13/5 find (2sinx - 3cosx)/(4sinx - 9cosx). 3
20) If 5tanx = 6 find (8sinx+ 3cosx)/(8sinx - 3cosx). 21/11
21) If 4cot x =5 find (5sinx - 3cosx)/(5sinx+ 2cosx). 1/6
22) If tanx = 3/4 find (4sinx - 2cosx)/(4sinx + 3cosx). 1/6
23) If tanA = m/n find m sinA + n cos A)/(m sinA - n cosA). (m²+n²)/(m² - n²)
24) If cot x = √3 find (cosec²x+ cot²x)/(cosec²x - sec²x). 21/8
25) If 3 cosx = 1 find (6sin²x+tan²x)/4 cosx. 10
26) If 4tanx = 3 find (4sinx-2cosx)/(4sinx+3cosx). 1/6
27) If √3tanx = 3 sinx find sin²x - cos²x. 1/3
28) If cosec x = 13/12 find (2sinx - 3cosx)/(4sinx - 9 cosx). 3
29) If tanx = 1/√7 find (cosec²x- sec²x)/(cosec²x+ sec²x). 3/4
30) If sinx = a/√(a²+b²) find cosx and tanx. b/√(a²+b²), a/b
31) If sec x = x + 1/4x show that secx + tanx = 2x or 1/x
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