Prove that (cot θ + cosec θ - 1 ) / (cot θ - cosec θ + 1) = (1 + cos θ) / sinθ
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Solution :-
Consider LHS
Writing cot Φ in terms of sin Φ and cosΦ
Taking LCM
Rearranging the terms
Rationalising the denominator
= RHS
LHS = RHS
QED
Identities used to prove
- cos² Φ + sin²Φ = 1
- cos² Φ = 1 - sin² Φ
- x² - y² = (x + y)(x - y)
- (x + y)² = x² + y² + 2xy
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