Question

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

Answer 1

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

$\implies cos ( \alpha + \beta ) = cos \: 90\degree$

$\implies \alpha + \beta = 90\degree$

$\implies \alpha + \beta - 2\beta = 90\degree - 2\beta$

$\implies \alpha - \beta = 90\degree - 2\beta$

$\implies sin( \alpha - \beta) = sin(90\degree - 2\beta )\\= cos 2\beta$

Therefore.,

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

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