Question

plzz solve this fast.... ..

Answer 1

Tan theta =a/b
a sin theta - b cos theta /a sin theta +b cos theta
Divide whole equation by cos
a sin /cos -b cos/cos
_________________
a sin /cos +b cos/cos

a×tan theta -b
____________
a×tan theta +b

a×a/b -b
_______
a×a/b+b

a^2/b-b
_______
a^2/b +b

Take LCM

a^2-b^2/b
_______
a^2+b^2/b

b in upper eq n in down eq cut it become
a^2-b^2
_______
a^2+b^2

Answer 2

tan∅ = $\frac{a}{b}$ ........[ Given ]

We Need to Prove $\frac{asin∅ - bcos∅}{asin∅ + bcos∅}$ = $\frac{a^{2} - b^{2} }{a^{2} + b^{2}}$

Proof 

We can write it like that asin∅/ bcos∅ - bcos∅/ asin∅

On simplifying We get tan∅ * tan∅ - 1/tan∅ * 1/tan∅
[ Because a/b = tan∅... sin∅/cos∅ = tan∅.... b/a = 1/tan∅ (reciprocal)... and cos∅/sin∅ = 1/tan∅

On multiplying we get tan²∅ - 1/tan²∅

so we know tan∅ = a/b 

so by putting value we get a² - b²/b² + a²

or we can write it like $\frac{a^{2} - b^{2} }{a^{2} + b^{2}}$

Hence Proved LHS = RHS