Question

If cosx+sinx=sqrt(2)cosx then show that cosx-sinx=sqrt(2)sinx

Answer 1

Hello,

We suppose cos (x)≠0 and sin(x)≠0

cos(x)+sin(x)=√2 cos(x)
==>1+tg(x)=√2
==>tg(x)=√2-1
==>1/tg(x)=1/(√2-1)
==>cos (x)/sin(x)= √2+1
==>cos(x)=sin(x)+√2*sin(x)
==>cos(x)-sin(x)=√2 sin(x)