Is sin theta minus cos theta = root 2 Sin Theta then prove that sin theta + cos theta is equals to root sin theta?

If #sintheta-costheta=sqrt(2)sintheta#, then prove that, #sintheta+costheta=-sqrt(2)costheta#

1 Answer
Mar 17, 2018

#sintheta+costheta=-sqrt(2)costheta#

Explanation:

Here,
#sintheta-costheta=sqrt(2)sintheta#
#=>sintheta-sqrt(2)sintheta=costheta#
#=>sintheta(1-sqrt(2))=costheta#
#=>sintheta[(1-sqrt(2))((1+sqrt(2))/(1+sqrt(2)))]=costheta#
#=>sintheta[(1-2)/(1+sqrt(2)))=costheta#
#=>sintheta(-1)=(1+sqrt(2))costheta#
#=>-sintheta=costheta+sqrt(2)costheta#
#=>-sintheta-costheta=sqrt(2)costheta#
#=>sintheta+costheta=-sqrt(2)costheta#