Mathematics: If sina+cosa=root2cosa then prove cosa-sina=root2sina

If sina+cosa=root2cosa then prove cosa-sina=root2sina

kelseyxxswd2932

10.01.2022

$\cos A - \sin A = \sqrt{2} \sin A$ (Proved)

Step-by-step explanation:

We are given that $\sin A + \cos A =\sqrt{2} \cos A$ and we have to prove that

$\cos A - \sin A = \sqrt{2} \sin A$ .

Now, $\sin A + \cos A =\sqrt{2} \cos A$

⇒ $\sin A = (\sqrt{2} - 1 ) \cos A$

⇒ $\sin A = \frac{(2 - 1)\times \cos A}{(\sqrt{2} + 1 )}$

{By rationalization}

⇒ $(\sqrt{2} + 1) \sin A = \cos A$

⇒ $\sqrt{2} \sin A + \sin A = \cos A$

⇒ $\cos A - \sin A = \sqrt{2} \sin A$ (Proved)

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pnewma16

07.06.2020

12/5 also 2.4

Step-by-step explanation:

12 divided by 4 = 2.4

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