Question

verify each identity:
cos(alpha+beta)cos(alpha-beta)=cos^2beta-sin^2alpha

Answer 1

the laws:
cos(alpha+beta) = cos(alpha)*cos(beta) - sin(alpha)*sin(beta)
cos(alpha-beta) = cos(alpha)*cos(beta) + sin(alpha)*sin(beta)
they would help you

Answer 2

i used those but i got stuck :(

Answer 3

why?
cos(alpha+beta)cos(alpha-beta)
= [cos(alpha)*cos(beta) - sin(alpha)*sin(beta)] * [cos(alpha)*cos(beta) + sin(alpha)*sin(beta)]
= [cos(alpha)*cos(beta)]^2 - [sin(alpha)*sin(beta)]^2
= [cos^2(alpha)*cos^2(beta)] - [sin^2(alpha)*sin^2(beta)]
since cos^2(alpha) = 1- sin^2(alpha)
and sin^2(beta) = 1-cos^2(beta) , then
= [cos^2(beta)-sin^2(alpha)*cos^2(beta)] - [sin^2(alpha)-sin^2(alpha)*cos^2(beta)]
then sin^2(alpha)*cos^2(beta) - sin^2(alpha)*cos^2(beta) = 0
so
= cos^2(beta) - sin^2(alpha)

Answer 4

ohhh ok :) thanks! i made a mistake in one of my steps

Answer 5

u r welcome