Question

If cos `(alpha+beta)=0`, then `sin(alpha-beta)`canbe reduced to :
(a) `cosbeta`
(b)`cos2beta`
( c) `sinalpha`
(d) `sin2alpha`

Answer 1

Given that , `cos(alpha+beta)=0=cos90^(@)`
`:. alpha+beta=90^(@)`
`:.alpha=90^(@)-beta`
`:.sin (alpha-beta)=sin[(90^(@)-beta)]=sin(90^(@)-2beta)=cos2beta`