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Question
Prove that:
cos2θ (1 + tan2θ)
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Solution
L.H.S. = cos2θ (1 + tan2θ)
= cos2θ × sec2θ ...[∵ 1 + tan2 θ = sec2 θ]
= \[\cos^{2}\theta\times\frac{1}{\cos^{2}\theta}\]
= 1
= R.H.S.
∴ cos2θ (1 + tan2θ) = 1
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Proof: L.H.S. = (sec θ – cos θ) (cot θ + tan θ)
= `(1/square - cos θ) (square/square + square/square)` ......`[∵ sec θ = 1/square, cot θ = square/square and tan θ = square/square]`
= `((1 - square)/square) ((square + square)/(square square))`
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= `square/(square square)`
= tan θ.sec θ
= R.H.S.
∴ L.H.S. = R.H.S.
∴ (sec θ – cos θ) (cot θ + tan θ) = tan θ.sec θ
