Question

`(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`

Answer 1

Correct Answer - 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`