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(sin 3theta+sin5theta+sin7theta+sin9thet...

`(sin 3theta+sin5theta+sin7theta+sin9theta)/(cos 3theta+cos 5theta+cos 7theta+cos9theta)` is equal to

A

`tan 3theta`

B

`cot 3theta`

C

`tan 6 theta`

D

`cot 6 theta`

Text Solution

Verified by Experts

The correct Answer is:
C
`(sin 3theta+sin 5theta+sin7theta+sin9theta)/(cos 3theta+cos 5theta+cos 7theta+cos 9theta)`
`=((sin 3theta+sin9theta)+(sin5theta+sin7theta))/((cos 3theta+cos 9theta)+(cos 5theta+cos7theta))`
`=(2sin 6thetacos3theta+2sin6thetacos theta)/(2cos 6thetacos 3theta+2cos 6thetacos theta)`
`=(2sin6theta(cos 3theta+cos theta))/(2cos 6theta(cos 3theta+cos theta))`
`=tan 6theta`
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