Question

If sin (A + B)= k sin (A - B), prove that
(k - 1) cot B = (k + 1) cot A.​

Answer 1

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proof is below.

Step-by-step explanation:

sin (A + B)= k sin (A - B)

or,  sin (A + B) / sin (A - B) = k /1

using componendo and dividendo then,

{sin (A+B) + sin(A- B)} / {sin (A+B) - sin(A- B)} = k+1 /k-1

or, 2 sin A cos B / 2 cos A sin B = k+1 /k-1  

or, tan A . cot B = k+1 /k-1

or. 1/cot A * cot B= k+1 /k-1

or cot B /cot A =k+1 /k-1

∴ ( k-1 ) cot B = ( k+1) cot A

Proved.

Answer 2

Answer:

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