if cosA + sinA =root2 cosA, p t cosA-sinA=root2 sinA - Maths - Introduction to Trigonometry

Question

if cosA + sinA =root2 cosA, p t cosA-sinA=root2 sinA

Ajanta Trivedi · Accepted Answer

given: $\cos A + \sin A = \sqrt{2} \cos A ........ (1)$

$\sin A = (\sqrt{2 - 1}) \cos A \frac{\sin A}{\cos A} = \sqrt{2} - 1 \tan A = \sqrt{2} - 1 \cot A = \frac{1}{\tan A}$

$\cot A = \frac{1}{\sqrt{2} - 1} = \frac{\sqrt{2} + 1}{(\sqrt{2} - 1) (\sqrt{2} + 1)} \cot A = \frac{\sqrt{2} + 1}{2 - 1} = \sqrt{2} + 1$

therefore LHS part of the required equation is:

$\cos A - \sin A = \sin A [\frac{\cos A - \sin A}{\sin A}] = \sin A [\cot A - 1] = \sin A [\sqrt{2} + 1 - 1] = \sqrt{2} \sin A$

= RHS

which is the required result.

hope this helps you.

cheers!!

if cosA + sinA =root2 cosA, p.t cosA-sinA=root2 sinA.