Question

if cos A + sin A =2 cos A , then prove that cos A - sin A = 2 sin A

Answer 1

the problem seems to be given wrongly.

cos A + SIn  A = 2 Cos A     =>     Sin A  =  Cos  A
                        =>      Tan A = 1  => A = π/4, 5π/4 
Then   Cos A -  Sin  A = 0     and Not  2 Sin A..

Answer 2

cos A + sin A =2 cos A

sinA=2cosA-cosA

sinA=cosA-----------------------------------1

cos A - sin A = 2 sin APutting the value of sinA in the equation

cosA-cosA= 0