If `sin x = 1/4 , pi/2 lt x lt pi`, find the values of `cos\ x/2 and tan\ x/2`.

If tanx=3/4, pi < x < (3pi)/2 , find the values of sin x/2 , cos x/2 and tan x/2.

If tan x = -(4)/(3), (pi)/(2) lt x lt pi , then find the value of sin(x/2), cos(x/2) and tan(x/2) .

if cos x= (-sqrt(15))/(4) " and " (pi)/(2) lt x lt pi find the value of sin x .

If tanx=-(4)/(3), (3pi)/(2) lt x lt 2pi , find the value of 9sec^(2)x-4 cot x .

If tanA=-3/4 and pi/2 lt A lt pi , find the values of the following: i) sin(A/2) ii) cos(A/2) , iii) tan(A/2)

If cosA=-3/5 and pi/2 lt A lt pi , find the values of the following: i) sin2A , ii) cos2A , iii) tan2A

In the interval pi/2 lt x lt pi, find the value of x for which the matrix [(2sinx,3), (1 ,2sinx)]

If sec x cos 5x+1=0 , where 0lt x lt 2pi , then x=

If cos x + sin x = a , (- (pi)/(2) lt x lt - (pi)/(4)) , then cos 2 x is equal to

If 0 lt x lt pi and cos x + sin x = 1/2 , then tan x is