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

Options

A. `cosbeta`
B. `cos2beta`
C. `sinalpha`
D. `sin2alpha`

Answer

B

Explanation

Given, `cos(alpha+beta)=0=cos 90^(@)` `[therefore cos90^(@)=0]`
`rArr alpha+beta=90^(@)`
`rArr alpha=90^(@)- beta`……………..(i)
Now, `sin(alpha-beta) = sin(90^(@)-beta-beta)` [put the value from Eq.(i)]
`=sin(90^(@)-2beta)`
`=cos2beta` `[therefore sin(90^(@)-theta)=costheta]`
Hence, `sin(alpha-beta)` can be reduced to `cos2beta`.