Question

1 - sin theta + cos theta whole square is equal to 2 into 1 + cos theta into 1 minus sin theta​

Answer 1

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PLS MARK ️R️INLIEST

Answer 2

Answer:

The proof is explained step-wise below :

Step-by-step explanation:

To prove : (1 - sinθ + cosθ)² = 2(1 + cosθ)(1 - sinθ)

Proof : Taking L.H.S.

(1 - sinθ + cosθ)²

Using the trinomial identity of whole square :

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

(1 - sinθ + cosθ)² = 1 + sin²θ + cos²θ - 2sinθ - 2sinθcosθ + 2cosθ

⇒ 1 + 1 - 2sinθ - 2sinθcosθ + 2cosθ

⇒ 2 - 2sinθ - 2sinθcosθ + 2cosθ

⇒ 2(1 - sinθ - sinθcosθ + cosθ)

⇒ 2(1 + cosθ)(1 - sinθ)

= R.H.S.

Hence Proved.