If `cos(alpha + beta)=0`, then sin`(alpha-beta)` can be reduced toA. ` – InterviewSolution

InterviewSolution

1.	If `cos(alpha + beta)=0`, then sin`(alpha-beta)` can be reduced toA. `cosbeta`B. `cos2beta`C. `sinalpha`D. `sin2alpha`
Answer» Correct Answer - B 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`.

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