Prove the following trigonometric identities. tan²θ-sin²θ=tan²θsin²θ
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Answer with Step-by-step explanation:
Given : tan²θ − sin²θ = tan²θ × sin²θ
L.H.S = tan²θ − sin²θ
= sin²θ/cos²θ – sin²θ
[By using the identity, tanθ = sinθ/cosθ ]
= sin²θ[ 1/cos²θ – 1]
= sin²θ[(1− cos²θ)/cos²θ]
= sin²θ/cos²θ × sin²θ
[By using the identity, (1 - cos²θ) = sin²θ]
= tan²θ × sin²θ
tan²θ − sin²θ = tan²θ × sin²θ
L.H.S = R.H.S
Hence Proved..
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FORMULAS USED:-
•1-COS^2=SIN^2
•TAN THETA=SIN THETA/COS THETA.
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