Show that for all real values of and .

MATHEMATICS · Subjective · CBSE · Mathematics · Trigonometric Functions · Trigonometric Functions

Problem

Show that (sin⁡αcos⁡β+cos⁡αsin⁡β)2+(cos⁡αcos⁡β−sin⁡αsin⁡β)2=1(\sin\alpha\cos\beta + \cos\alpha\sin\beta)^2 + (\cos\alpha\cos\beta - \sin\alpha\sin\beta)^2 = 1 for all real values of α\alpha and β\beta.

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