Question

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Answer 1

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Answer 2

$cos( \alpha - \beta )-cos( \alpha + \beta )=2sin \alpha sin \beta$
$cos \alpha *cos \beta +sin \alpha*sin \beta-(cos \alpha *cos \beta -sin \alpha*sin \beta)=2sin \alpha sin \beta$
$cos \alpha *cos \beta +sin \alpha*sin \beta-cos \alpha *cos \beta+sin \alpha*sin \beta=2sin \alpha sin \beta$
$sin \alpha*sin \beta-+sin \alpha*sin \beta=2sin \alpha sin \beta$
$2sin \alpha*sin \beta=2sin \alpha sin \beta$

2) $cos(60- \alpha )-cos( 60+\alpha )= \sqrt{3} sin \alpha$
$cos60cos \alpha +sin60sin \alpha-(cos60cos \alpha -sin60sin \alpha)= \sqrt{3} sin \alpha$
$cos60cos \alpha +sin60sin \alpha-cos60cos \alpha +sin60sin \alpha= \sqrt{3} sin \alpha$
$sin60sin \alpha +sin60sin \alpha= \sqrt{3} sin \alpha$
$2sin60sin \alpha = \sqrt{3} sin \alpha$
$2* \frac{ \sqrt{3} }{2} sin \alpha = \sqrt{3} sin \alpha$
$\sqrt{3} sin \alpha = \sqrt{3} sin \alpha$

3) $sin30*cos \alpha -sin \alpha *cos30+sin30*cos \alpha +sin \alpha cos30=cos \alpha$
$sin30*cos \alpha +sin30*cos \alpha =cos \alpha$
$2sin30*cos \alpha =cos \alpha$
$2* \frac{1}{2} cos \alpha =cos \alpha$
$cos \alpha =cos \alpha$