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प्रश्न
Prove that sec2θ – cos2θ = tan2θ + sin2θ
उत्तर
L.H.S = sec2θ – cos2θ
= sec2θ – (1 – sin2θ) ......`[(because sin^2theta + cos^2theta = 1),(therefore 1 - sin^2theta = cos^2theta)]`
= sec2θ – 1 + sin2θ
= tan2θ + sin2θ ......`[(because 1 + tan^2theta = sec^2theta),(therefore tan^2theta = sec^2theta - 1)]`
= R.H.S
∴ sec2θ – cos2θ = tan2θ + sin2θ
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