Question

if 2sin2Q - cos2Q=2, find the value of Q

Answer 1

Solution :

2 sin2Q - cos 2Q = 2

Squaring the equation,  we get,

4 sin²2Q + 4 cos²2Q - 4 sin2QCOS2Q = 4

4 (sin²2Q  + cos²2Q)  - 4 = 4sin2Qcos2Q

4-4=2x (2 sin2Qcos2Q)          (∵ sin²2Q  + cos²2Q =1)

0 = 2 x sin4Q       (∵ sin4Q = 2sin2Qcos2Q )

sin4Q = 0

4Q = 90°

Q= 45°