Question

If cos (α + β) = 0, then sin (α – β) can be reduced to (A) cos β (B) cos 2β (C) sin α (D) sin 2α

Answer 1

here is the option is (B)

Answer 2

$Given \: cos ( \alpha + \beta ) = 0$

$\implies cos ( \alpha + \beta ) = cos 90\degree </p><p>$

$\implies \alpha + \beta = 90\degree </p><p>$

$\implies \alpha = 90\degree - \beta \: --(1)$

$Now, sin ( \alpha - \beta ) \\= sin (90 - \beta - \beta ) \:[From \: (1) ]$

$= sin ( 90 - 2\beta) \\= cos 2\beta$

Therefore.,

$\red{sin ( \alpha - \beta ) }= \green {cos 2\beta }$

$Option \: { (B) } \: is \: correct .$

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