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If 5(tan^2x - cos^2x)=2cos 2x + 9, then ...

If `5(tan^2x - cos^2x)=2cos 2x + 9`, then the value of cos4x is

A

`- (7)/(9)`

B

`- (3)/(5)`

C

`(1)/(3)`

D

`(2)/(9)`

Text Solution

Verified by Experts

The correct Answer is:
A
`5 ( tan ^(2) x - cos^(2) x) = 2 cos 2x + 9`
`rArr 5 (sec^(2) x -1- cos ^(2)x) = 2(2 cos^(2)x -1)+9`
`rArr 5[(1)/(y)-1-y] = 2(2y-1)+9` (Putting `cos^(2)x =y` )
`rArr 9y^(2) + 12y -5 =0`
`rArr (3y -1)(3y +5) =0`
`rArr y = (1)/(3)" " (because y =-(5)/(3)` is not possible `)`
Now, `cos 2x = 2 cos^(2) x -1 = 2 ((1)/(3)) -1 =- (1)/(3)`
`" " cos 4x = 2cos ^(2)2x -1 = 2 (- (1)/(3))^(2) - 1 = - (7)/(9)`
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