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Trigonometric Identity and Ratio
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Trigonometric Ratios

Example: If cos + sin = 2 cos , show that cos - sin = 2 sin .
Solution: We have,
cos + sin = 2 cos
(cos + sin )2= 2 cos2
cos2 + sin2 + 2 cos sin = 2 cos2
cos -2 cos sin = sin
cos2 - 2 cos sin + sin2 = 2 sin2
(cos - sin )2 = 2 sin2
cos -sin = 2sin
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