Question

(sina.Cosb + cosa.Sinb)^2+(cosa.Cosb-sina.Sinb)^2=1 , prove that

Answer 1

from L. H. S. =
$( \sin( \alpha ) \cos( \beta ) + \cos( \alpha ) \sin( \beta )) {}^{2} + ( \cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta ) ) {}^{2} \\ \\ = \sin {}^{2} ( \alpha + \beta ) + \cos {}^{2} ( \alpha + \beta ) \\ \\ = 1$
=R. H. S

proved.

hope it helps..