If sin 2 θ cos 2 θ (1 + tan 2 θ ) (1 + cot 2 θ ) = λ , then find the value of λ .

Question

Philoid · Accepted Answer

Given: sin²θ cos²θ (1 + tan²θ) (1 + cot²θ) = λ

To find: λ

We know that 1 + tan² θ = sec² θ

And 1 + cot² θ = cosec² θ

⇒ sin²θ cos²θ (1 + tan²θ) (1 + cot²θ)

= sin² θ cos² θ sec² θ cosec² θ

Now, ∵

And ∵

⇒ sin² θ cos² θ (1 + tan² θ) (1 + cot² θ)

= sin² θ cos² θ sec² θ cosec² θ

⇒ λ = 1