If 5(tan^2 x – cos^2x) = 2cos2x + 9, then the value of cos4x is :

Question

(1)-3/5
(2) 1/3
(3) 2/9
(4) -7/9

Answer 1

Answer is -7/9

5 (tan²x - cos²x) = 2cos2x +9 

5 ( (sec²x - 1) - cos²x) = 2(2cos²x - 1) +9 

5 (1/cos²x - 1- cos²x) = 4cos²x - 2 + 9 

5 (1 - cos²x - cos⁴x ) = 4cos⁴x + 7cos²x 

You solve this we get = 9cos⁴x+12cos²x-5 

Therefore let cos⁴x =y² and cos²x = y. 

0=9y² + 12y - 5

You will get the answer by solving for y