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Number of solutions of the equation cos...

Number of solutions of the equation ` cos^(4) 2x + 2 sin^(2) 2x=17( cos x+ sin x)^(8), o lt x lt 2 pi ` is

A

4

B

8

C

10

D

16

Text Solution

Verified by Experts

The correct Answer is:
A
Let `sin 2x=y`, then `1+y^(2)=17(1+y)^(4)`
`rArr y= sin 2x=-1//2`
`rArr x=105^(@), 165^(@), 285^(@), 345^(@)`
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