Question

If sin²θ cos²θ θ (1 + tan²θ ) (1 + cot² θ) = λ, then find the value of λ.

Answer 1

Answer:

The value of λ  is 1 .  

Step-by-step explanation:

Given : sin²θ  cos²θ θ (1 + tan²θ ) (1 + cot² θ) = λ

sin²θ  cos²θ (sec²θ ) (cosec² θ) = λ

[By using an  identity,1 + tan² θ = sec² θ ,cot² θ + 1 = cosec² θ]

(sin²θ  × cosec² θ) × (cos²θ × sec²θ ) = λ

(sin²θ  × 1/sin² θ) × (cos²θ × 1/cos²θ ) = λ

[cosecθ = 1/ sinθ, secθ = 1/cosθ]

1 × 1 = λ

λ = 1

Hence, the value of λ  is 1 .  

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Answer 2

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The above attachment contains step-by-step-explanation with answer.

➟ λ = 1

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