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Question
Prove the following:
cot2 θ − cos2 θ = cot2 θ.cos2θ
Theorem
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Solution
LHS = cot2 θ − cos2 θ
= `cos^2θ/sin^2θ - cos^2θ`
= `cos^2θ(1/(sin^2θ) - 1)`
= `cos^2θ((1- sin^2θ)/sin^2θ)`
∴`cos^2θ/sin^2θ.cos^2θ = cot^2 θ.cos^2θ`
∴ LHS = RHS
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