Question

Show that cos^2(45+x)-sin^2(45-x)=0 .

Answer 1

LHS = cos^2 ( 45+x)
= (cos{45+x})^2
= {sin(90-(45+x))}^2
= { sin ( 45 - x)}^2
= sin^2 ( 45-x)
= RHS

Hence,proved.

Answer 2

Step-by-step explanation:

LHS= cos²(45+x) - sin²(45-x)

(cos(45+x))²-(sin(45-x))²

=(cos(45+x))² - (sin(1×90-(45+x)))²

=(cos(45+x))² - (cos(45+x))²

=cos²(45+x) - cos²(45+x)

=0 = RHS (proved)