Question

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

Answer 1

i didn't understand the question

Answer 2

Question :- if sin(A + B) = k sin(A - B), prove that (k - 1) cot B = (k + 1) cot A ?

Solution :-

→ sin(A + B) = k * sin(A - B)

using :-

• In LHS :- sin(A + B) = sin A * cos B + cos A * sin B
• In RHS :- sin(A - B) = sin A * cos B - cos A * sin B

→ sin A * cos B + cos A * sin B = k * (sin A * cos B - cos A * sin B)

→ sin A * cos B + cos A * sin B = k * sin A * cos B - k * cos A * sin B

→ cos A * sin B + k * cos A * sin B = k * sin A * cos B - sin A * cos B

→ cos A * sin B (1 + k) = sin A * cos B (k - 1)

→ (cos A / sin A) (1 + k) = (cos B/sin B) (k - 1)

using :-

• cos θ / sin θ = cot θ

→ cot A (k + 1) = cot B (k - 1)

→ (k - 1) cot B = (k + 1) cot A (Proved)

Learn more :-

It sino + tano = m

tano - sino an

Then express the

values of m²-n² in terms

of M and N

https://brainly.in/question/13926306

tanA/(1-cotA) + cotA/(1-tanA)

https://brainly.in/question/16775946