Question

If cos( alpha + beeta )= 0, then sin( alpha - beeta ) can be reduced to ?

Answer 1

since

cos(alpha + beeta) =0,

cos(alpha+beeta)=cos90°,

then

alpha+beeta=90°,

then

alpha = 90° - beeta,

therefore

sin(alpha-beeta)=sin(90°-beeta-beeta),

=sin(90°-2beeta),

=cos2beeta