Question

(1-2sina.cosa)/2=sin²(45-a)

Answer 1

Answer:

see answer in attachment....

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Answer 2

EXPLANATION.

Prove that.

⇒ [(1 - 2sin A cos A)/(2)] = sin²(π/4 - A).

As we know that,

Identities :

⇒ sin(α - β) = sinα cosβ - cosα sinβ.

Using this identities in this question, we get.

We solve R.H.S of the expression, we get.

⇒ sin²(π/4 - A) = sin²(45° - A).

⇒ sin²(45° - A) = [sin45° cos A - cos45° sin A]².

⇒ sin²(45° - A) = [1/√2 cos A - 1/√2 sin A]².

⇒ sin²(45° - A) = 1/2(cos A - sin A)².

⇒ sin²(45° - A) = 1/2(cos²A + sin²A - 2sinAcosA).

⇒ sin²(45° - A) = 1/2(1 - 2sinAcosA).

Hence Proved.