Question

Sinx+siny=2 then cos(x+y)=?

Answer 1

Answer:

$\sin( \alpha ) + \sin( \beta ) = 1 \\ \cos( \alpha + \beta ) = \cos( \alpha ) \cos( \beta ) - \sin( \alpha ) \sin( \beta ) \\ sin \alpha + sin \beta = 1 \: when \: \alpha = \beta = 90 \\ so \: sin \alpha \ \times sin( \beta ) = 1 \times 1 = 1 \\ \cos( \alpha + \beta ) = \cos(90) . \cos(90) - 1 \\ \: \: \: \: \: = 0 - 1 = ( - 1)$