Question

Given if tan(a) =p/q
Then prove that

$\frac{p \sin(a) + q \cos(a) }{p \sin(a) - q \cos(a) } = \frac{ {p}^{2} + {q}^{2} }{ {p}^{2} - {q}^{2} }$
Answer only with detailed steps.

NO SPAMMING

Answer 1

Hope you get the answer.

Answer 2

tan A = p/q

tan A = p/q
⇒ sin A / cos A = p/q
⇒ sin A = p/q cos A

(p sin A +q cos A) / (p sin A - q cos A)

= (p × p/q cos A) +(q cos A) / (p × p/q cos A) - (q cos A)

= (p2/q) + (q) / (p2/q) - (q)

= (p2 +q2) / (p2 -q2)

∴ (p sin A +q cos A) / (p sin A -q cos A) = (p2 + q2) / (p2 - q2).

this is your answer.....

it is helpful for you....