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The number of solution satisfying the eq...

The number of solution satisfying the equations `tan 4theta=cot 5theta` and `sin 2theta=cos theta` in `[0,2pi]` is

A

2

B

3

C

4

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
`sin 2 theta = cos theta` or `2 sin theta cos theta - cos theta =0`
`rArr cos theta (2 sin theta - 1)=0`
`rArr cos hteta = 0` or `sin theta =(1)/(2)`
`rArr theta =(pi)/(2), (3pi)/(2),(pi)/(6),(5pi)/(6)` all four satisfying first equation.
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