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Question
Prove that: `(1 - tan^2 θ)/(1 + tan^2 θ) = cos^2 θ - sin^2 θ`
Theorem
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Solution
LHS = `(1 - tan^2 θ)/(1 + tan^2 θ)`
= `(1 - tan^2 θ)/(sec^2 θ)`
= `1/(sec^2 θ) - (tan^2 θ)/(sec^2 θ)`
= `cos^2 θ - (sin^2 θ)/(cos^2 θ) xx cos^2 θ `
= cos2 θ – sin2 θ
= RHS
Hence Proved.
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