Question

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

Answer 1

Correct Answer - 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 ".`