plzz solve this fast.... ..
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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
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
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tan∅ = ........[ Given ]
We Need to Prove =
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
Hence Proved LHS = RHS
We Need to Prove =
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
Hence Proved LHS = RHS
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