How to solve this trigonometric equation?

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1 Answer
Apr 1, 2018

Answer is (3).

Explanation:

5(tan2xcos2x)=2cos2x+9

5(sec2x1)5cos2x=2(2cos2x1)+9

or 5sec2x9cos2x12=0 and multiplying by cos2x we get

59cos4x12cos2x=0

i.e. 9cos4x+12cos2x5=0

and cos2x=12±144+18018

= 12±1818

i.e. cos2x=13 as we cannot have cos2x as negative

Hence cos2x=2cos2x1=2131=13

and cos4x=2cos22x1=2(13)21=79

Hence, answer is (3).