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प्रश्न
If sin2 θ cos2 θ (1 + tan2 θ) (1 + cot2 θ) = λ, then find the value of λ.
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उत्तर
Given:
`sin ^2θ cos^2 θ(1+tan^2 θ)(1+cot ^2θ)=λ`
`⇒ sin^2θ cos^2 θ sec^2 θ cosec^2θ=λ`
⇒`(sin^2 θ cosec^2θ )xx (cos^2θ sec^2 θ)= λ`
⇒ `(sin^2θ xx 1/sin^2θ )(cos^2 θxx1/cos^2θ)=λ`
\[\Rightarrow \lambda = 1 \times 1 = 1\]
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