Answer:
[tex]\cos A - \sin A = \sqrt{2} \sin A[/tex] (Proved)
Step-by-step explanation:
We are given that [tex]\sin A + \cos A =\sqrt{2} \cos A[/tex] and we have to prove that
[tex]\cos A - \sin A = \sqrt{2} \sin A[/tex].
Now, [tex]\sin A + \cos A =\sqrt{2} \cos A[/tex]
⇒ [tex]\sin A = (\sqrt{2} - 1 ) \cos A[/tex]
⇒ [tex]\sin A = \frac{(2 - 1)\times \cos A}{(\sqrt{2} + 1 )}[/tex]
{By rationalization}
⇒ [tex](\sqrt{2} + 1) \sin A = \cos A[/tex]
⇒ [tex]\sqrt{2} \sin A + \sin A = \cos A[/tex]
⇒ [tex]\cos A - \sin A = \sqrt{2} \sin A[/tex] (Proved)
