Question

cosx+sinx=√2cosx then show that cosx-sinx=2sinx​

Answer 1

cosx + sinx = √2cosx. ( given )

squaring both sides

cos²x+sin²x+2sinxcosx=2cos²x

1+2sinxcosx=2cos²x

2sinxcosx =2cos²x-1

2sinxcosx=2cos²x-sin²x-cos²x

2 sinxcosx=cos²-sin²x (1)

cosx-sinx

squaring the above expression

cos²x+sin²x-2sinxcosx

sin²+cos²x-cos²x+sin²x

2sin²x

hope it helps