Question

If cosa - sina= √2sina,then prove that cosa + sina= √2cosa

Answer 1

hope it will help you....

Answer 2

Answer:

Proved is given below.

Step-by-step explanation:

Given that $cos a - sin a =\sqrt2 sina$

we have to prove $cos a + sin a =\sqrt 2 cos a$

$cos a - sin a =\sqrt2 sina\\\\cosa=\sqrt2sina+sina\\\\sina=\frac{coaa}{\sqrt2+1}$

By rationalizing, we get

$sina=\frac{cosa}{\sqrt2+1}\times\frac{\sqrt2-1}{\sqrt2-1}=\frac{(\sqrt2-1)cosa}{(\sqrt2)^2-1^2}=(\sqrt2-1)cosa$

⇒ $sina=\sqrt2cosa-cosa$

⇒ $sina+cosa=\sqrt2cosa$

Hence proved.