Question

If sin∆ = n sin (∆+ 2¶) then tan (∆+ ¶) s equal to
a) (1 - n/2 -n)tan¶
b) (1 + n/1 - n) tan¶
c) tan¶
d) (1 - n/1 + n)tan¶
Answer with proper explaination
Hint : use factorisation defactorisation fromula​

Answer 1

sinθ=nsin(θ+2α)

 sin(θ+2α)sinθ=n

 apply componendo dividendo rule, 

sinθ−sin(θ+2α)sinθ+sin(θ+2α)=n−1n+1

 apply sinC+sinD and sinC−sinD 

 2sinαcos(θ+α)2sin(θ+α)cosα=n−1n+1 

tanαtan(θ+α)=n−1n+1

tan(θ+α)=n−1n+1tanα

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