If-msin-nsin-2-then-tan-cot-equal-to-Answer-given-in-my-book-is-1-n-1-n-

Question Number 13249 by Tinkutara last updated on 17/May/17

If m \sin θ = n \sin (θ + 2 α), then

\tan (θ + α) \cot α equal to

[Answer given in my book is \frac{1 - n}{1 + n}]

Commented by prakash jain last updated on 17/May/17

\tan (θ + α) \cot α

= \frac{\sin (θ + α)}{\cos (θ + α)} . \frac{\cos α}{\sin α}

\sin A \cos B = \frac{1}{2} (\sin (A + B) + \sin (A - B))

= \frac{\frac{\sin (θ + 2 α) + \sin θ}{2}}{\frac{\sin (θ + 2 α) + \sin (- θ)}{2}}

= \frac{\sin (θ + 2 α) + \sin θ}{\sin (θ + 2 α) - \sin θ}

a s s u m i n g s i n θ \neq 0

= \frac{\frac{\sin (θ + 2 α)}{\sin θ} + 1}{\frac{\sin (θ + 2 α)}{\sin θ} - 1} = \frac{m + n}{m - n}

The answer does not match with

ur book . I will recheck later .

Commented by Tinkutara last updated on 18/May/17

I was reaching on this same solution .

Maybe answer in my book is wrong .