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(sin 5theta+ sin 2theta- sin theta)/(cos...

`(sin 5theta+ sin 2theta- sin theta)/(cos5theta+2cos3theta+2cos^2theta+costheta)` is equal to

A

`tan theta`

B

`cos theta`

C

`cot theta`

D

none of these

Text Solution

Verified by Experts

LHS`=(2sin 2 theta cos 3 theta+sin 2 theta)/(2 cos 3 theta,cos 2 theta+2 cos 3 theta+2 cos ^(2)theta)=(sin 2theta[2 cos 3 theta+1])/(2[cos 3 theta(cos 2 theta+1)+(cos ^(2)theta)])`
`=(sin2 theta[2 cos 3 theta+1])/(2[cos 3 theta(2 cos ^(2)theta)+cos^(2)theta])=(sin2 theta(2 cos 3 theta+1))/(2 cos^(2)theta(2 cos 3 theta+1))=tan theta`
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