Question #b3c4d

1 Answer
Jan 2, 2018

The given hypothesis does not appear to be true.

Explanation:

If #sin(theta)+cos(theta)=sqrt(2)cos(theta)#
then
#color(white)("XXX")(sin(theta))/(cos(theta))+1=sqrt(2)#

#color(white)("XXX")tan(theta)=sqrt(2)-1#

#color(white)("XXX")theta=arctan(sqrt(2)-1)~~0.392699082#

But
#color(white)("XXX")sqrt(2) * cos(0.392699082) ~~1.306562925#
and
#color(white)("XXX")sqrt(2) * sin(0.392699082)~~0.5411961#
which are not equal