Question

If cosec²θ (1 + cos θ) (1 − cos θ) = λ, then find the value of λ.

Answer 1

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Answer 2

Answer:

The value of λ  is 1 .  

Step-by-step explanation:

Given :  cosec²θ (1 + cos θ) (1 − cos θ) = λ

cosec²θ [(1 + cos θ) (1 − cos θ)] = λ

cosec²θ (1 − cos² θ)  = λ

[By using identity , (a + b) (a - b) = a² - b²]

cosec² θ (1 − cos² θ)  = λ

cosec² θ (sin² θ)  = λ

[By using the identity, (1 - cos²θ) = sin²θ]

1/sin²θ × sin²θ = λ

[cosecθ = 1/ sinθ]

1= λ

λ = 1

Hence, the value of λ  is 1 .  

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