We know that cos2x=cos²x-sin²x
=cos²x-(1-cos²x) [since, cos²x+sin²x=1]
=cos²x-1+cos²x
=2cos²x-1
So, cos2x=2cos²x-1
Hence, cos²x= (1+cos2x)/2
Trigonometric Identities are useful whenever trigonometric functions are involved in an expression or an equation. Trigonometric Identities are true for every value of variables occurring on both sides of an equation. Geometrically, these identities involve certain trigonometric functions (such as sine, cosine, tangent) of one or more angles.
Most common trigonometric identities are:
- cos²x + sin²x = 1
- sec²x - tan²x = 1
- cosec²x - cot²x = 1
- cos2x = cos²x - sin²x
Therefore we get that the statement cos² x = (1 - cos 2x)/2 is false.
Learn more about trigonometric identities here-
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