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Choose the correct answer in each of the following questions: If `cos (alpha + beta)=0 " then " sin(alpha -beta)=?`

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Choose the correct answer in each of the following questions:
If `cos (alpha + beta)=0 " then " sin(alpha -beta)=?`
A. `sin alpha`
B. `cos beta`
C. `sin 2 alpha`
D. `cos 2 beta`
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1 Answer

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Best answer
Correct Answer - D
`cos(alpha+beta)=0rArr alpha +beta=90^(@)rArr alpha=90^(@)-beta`
`therefore (alpha-beta)=(90^(@)-2beta)rArr sin(alpha-beta)=sin(90^(@)-2beta)=cos2beta.`
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