Question

if cosa + sina =√2cosa. show that cosa - sina=√2sina.​

Answer 1

Step-by-step explanation:

$\sin( \alpha ) + \cos( \alpha ) = \sqrt{2} \cos( \alpha ) \\ 1 + 2 \sin( \alpha ) \cos( \alpha ) = 2 { \cos( \alpha ) }^{2} \\ = > 1 - { \cos( \alpha ) }^{2} = { \cos( \alpha ) }^{2} - 2 \sin( \alpha ) \cos( \alpha ) \\ = > { \sin( \alpha ) }^{2} + { \sin( \alpha ) }^{2} = { \cos( \alpha ) }^{2} + { \sin( \alpha ) }^{2} - 2 \sin( \alpha ) \cos( \alpha ) \\ = > 2 { \sin( \alpha ) }^{2} = {( \sin( \alpha ) - \cos( \alpha ) )}^{2} \\ = > \sqrt{2} \sin( \alpha ) = \sin( \alpha ) - \cos( \alpha )$

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