Prove that
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Question :-
Answer :-
(sinθ + cosθ)^2 + (sinθ - cosθ)^2/(sinθ)^2 - (cosθ)^2
sin^2θ+ cos^2 θ+ 2sinθcosθ+ sin^2 θ+ cos^2θ - 2sinθcosθ/ sin^2θ- cos^2θ
1 + 2sinθcosθ + 1 - 2sinθcosθ/ sin^2 θ- cos^2 θ
2/ sin^2 θ- cos^2θ
2/ cos^2 θ(sin^2θ/cos^2θ - 1)
2/cos^2θ(tan^2θ-1)
= 2sec^2θ/tan^2θ-1
Therefore, LHS = RHS
Hence proved !
Answered by
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Answer:
hi mates this is ur answer
Step-by-step explanation:
➡️➡️sinθ + cosθ)² + (sinθ - cosθ)²/(sinθ)² - (cosθ)²
➡️➡️sin²θ+ cos²θ+ 2sinθcosθ+ sin²θ+ cos²θ - 2sinθcosθ/ sin²θ- cos²θ
➡️➡️1 +2sinθcosθ + 1- 2sinθcosθ/sin² θ- cos² θ²/ sin²θ- cos²θ
➡️➡️2/ cos²θ(sin²θ/cos²θ - 1)
➡️➡️2/cos²θ(tan²θ-1)
✍✍= 2sec²θ/tan²θ-1
✍✍ LHS = RHS✍✍
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