Question

If sin² θ cos² θ (1 + tan² θ) (1 + cot² θ) = λ, then find the value of λ. 

Answer 1

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`

\[\Rightarrow \lambda = 1 \times 1 = 1\]