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If 5tan2xcos2x=2cos2x+9 then the value of cos4x is 

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13
b
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c
79
d
35

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detailed solution

Correct option is C

5tan2xcos2x=2cos2x+9

Let u=tan2xwe have

5u11+u=21u1+u+9 5u2+u1=22u+9+9: 5u22u16=0(5u+8)(u2)=0

But u is positive u=2

Now, tan2x=2

cos2x=1tan2x1+tan2x=121+2=13cos4x=2cos22x1=2191=79

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