Question

If sin x =n sin (x+2alpha) prove that tan (x+alpha)=1+n÷1-n tanalpha​

Answer 1

Explanation:

We have,

sinx=nsin(x+2α)

⇒

sinx

sin(x+2α)

=

n

1

⇒

sin(x+2α)−sinx

sin(x+2α)+sinx

=

1−n

1+n

.(using componendo and dividendo)

⇒

2sinαcos(x+α)

2sin(x+α)cosα

=

1−n

1+n

⇒tan(x+α)=

1−n

1+n

tanα

Answer 2

Answer is following .