Question

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prove this one:-
$\sin(a) + \cos(a) = \sqrt{2} \cos(a)$
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Answer 1

cos θ + sin θ = √2 cos θ

sin θ = √2 cos θ - cos θ

sin θ = ( √2 - 1 ) cos θ

= [ sin θ / ( √2 - 1 ) ] = cos θ

= [ sin θ ( √2 + 1 ) / ( 2 - 1 ) ] = cos θ

 We rationalized the denominator in the 2nd step  

=> [ √2 sin θ + sin θ ] = cos θ

=> cos θ - sin θ = √2 sin θ

Answer 2

Answer:

see image for answer

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