How do you prove (sinx - cosx)^2 +(sin x + cosx)^2 = 2?
2 Answers
May 4, 2018
Explanation:
red terms equal 1
from the Pythagorean theorem
also, blue terms equal 1
So
green terms together equal 0
So now you have
True
May 4, 2018
Explanation:
"using the "color(blue)"trigonometric identity"
•color(white)(x)sin^2x+cos^2x=1
"consider left side"
"expand each factor using FOIL"
(sinx-cosx)^2=sin^2xcancel(-2cosxsinx)+cos^2x
(sinx+cosx)^2=sin^2xcancel(+2cosxsinx)+cos^2x
"adding the right sides gives"
2sin^2x+2cos^2x
=2(sin^2x+cos^2x)
=2xx1=2=" right side "rArr"proven"