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If thetain(0,2pi) then number of solutio...

If `thetain(0,2pi)` then number of solution of the equation`cos^(4)2theta+2sin^(2)2theta=17(sintheta+costheta)^(8)` is greater than of equal to

A

2

B

3

C

4

D

5

Text Solution

Verified by Experts

The correct Answer is:
A
`Let sin2theta=t`
`1+t^(4)=17(1+t)^(4)`
`8y^(2)+34y+35=0" where "y=t+(1)/(t)`
Solving :`y=-(5)/(2)`
`:.t=-(1)/(2)`
`sin2theta=-(1)/(2)`
`:.theta=(7pi)/(12),(11pi)/(12),(19pi)/(12),(23pi)/(12)`
`:.4" sollutions ".`
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