Question:
Cos20 2sin^2 55 -√2 sin65. =
Answer:
Given, cos 20 + 2sin2 55 - √2 sin65
= cos 20 + 1 - cos 110 - √2 sin65 {since cos 2x = 1 - 2sin2 x}
= 1 + cos 20 - cos 110 - √2 sin65
= 1 - 2 * sin {(20 + 110)/2 * sin{(20 - 110)/2} - √2 sin65 {Apply cos C - cos D formula}
= 1 - 2 * sin 65 * sin (-45) - √2 sin65
= 1 + 2 * sin 65 * sin 45 - √2 sin65
= 1 + (2 * sin 65)/√2 - √2 sin65
= 1 + √2 ( sin 65 - √2 sin 65
= 1
So, cos 20 + 2sin2 55 - √2 sin65 = 1
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