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What is the value of cos[(180° – θ)/2].cos[(180° – 9θ)/2] + sin[(180° – 3θ)/2].sin[(180° – 13θ)/2]?

What is the value of cos[(180° – θ)/2].cos[(180° – 9θ)/2] + sin[(180° – 3θ)/2].sin[(180° – 13θ)/2]? Correct Answer cos2θ.cos6θ

cos.cos + sin.sin

⇒ sinθ/2.sin9θ/2 + cos3θ/2.cos13θ/2

We know the formulas;

2sinA.sinB = cos(A – B) – cos(A + B)

2cosA.cosB = cos(A + B) + cos(A – B)]

⇒ /2

⇒ /2

⇒ 2cos6θ.cos2θ/2

⇒ cos6θ.cos2θ

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