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Solution :

We have to find what is (secθ - tanθ)² (1 + sinθ) equal to?

Given trigonometric expression :

→ (secθ - tanθ)² (1 + sinθ)

We know the trigonometric ratios :

secθ = 1/cosθ

tanθ = sinθ/cosθ

Also, sin² A = 1 - cos² A

So using these,

→ [1/cosθ - (sinθ/cosθ)]² (1 + sinθ)

→ [(1 - sinθ)/cosθ]² (1 + sinθ)

→ [(1 - sinθ)²/cos² θ] (1 + sinθ)

→ [(1 - sinθ)²/(1 - sin² θ)] (1 + sinθ)

→ [(1 - sinθ)(1 - sinθ)/(1 + sinθ)(1 - sinθ)] (1 + sinθ)

→ [(1 - sinθ)/(1 + sinθ)] (1 + sinθ)

1 + sinθ gets cancelled,

→ 1 - sinθ

So therefore, answer is (3) 1 - sinθ.

Answer:

Correct answer is :- (3) 1-sin∅

Step-by-step explanation:

See the above provide photo . It has step by step prove .

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