If cos A + sin A = (√2) cos A, prove that cos A − sin A = (√2) sin A
given
cos A + sin A = (√2) cos A
sin A = (√2) cos A - cos A
sin A = (√2 - 1 ) cos A
sin A/ (√2 - 1 ) = cos A
rationalising
(√2 + 1 ) sin A/ [ (√2 - 1 ) (√2 + 1 ) ] = cos A
(√2 + 1 ) sin A / [2-1] = cosA
(√2 + 1 ) sin A / [1] = cosA
(√2 + 1 ) sin A = cosA
apply distribution law
(√2) sin A + 1 sinA = cosA
(√2) sin A + sin A = cosA
(√2) sin A = cosA - sin A
OR
cos A − sin A = (√2) sin A
cbse 10th maths old board exam question paper 2025 2026 trigonometry
video of an alternate method
