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If x in [-(5pi)/2,(5pi)/2], then the gre...

If `x in [-(5pi)/2,(5pi)/2]`, then the greatest positive solution of `1+sin^4x=cos^2 3x` is -

A

`pi`

B

`2pi`

C

`(5pi)/(2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `1=cos^(2)3x=sin^(4)x`
`rArrsin^(2)3x+sin^(4)x=0`
`rArr{3sinx-4sin^(3)x}^(2)+sin^(4)x=0`
`rArrsin^(2)x{(3-4sin^(2)x)^(2)+sin^(2)x}=0`
`thereforesinx=0rArrx=npi`
Hence , greatest positive solution is `2pi`.
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