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प्रश्न
Prove that `(cos θ - 2 cos^3 θ)/(sin θ - 2 sin^3 θ) + cot θ = 0`.
सिद्धांत
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उत्तर
L.H.S. = `(cos θ - 2 cos^3 θ)/(sin θ - 2 sin^3 θ) + cot θ`
= `(cos θ(1 - 2 cos^2 θ))/(sin θ (1 - 2 sin^2 θ)) + cot θ`
= `cot θ ((sin^2 θ + cos^2 θ - 2 cos^2 θ))/((sin^2 θ + cos^2 θ - 2 sin^2 θ)) + cot θ`
= `- cot θ ((sin^2 θ - cos^2 θ))/((cos^2 θ - sin^2 θ)) + cot θ`
= −cot θ + cot θ
= 0
L.H.S. = R.H.S.
Hence proved.
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