cos^2 (a+x) -sin^2 a=cos x * cos(2a+x)
see
http://www.jiskha.com/display.cgi?id=1235346549
don't tell my I did all that work, and you didn't even look at it.
i posted a sorry. i posted this twice on that one. And i don't understand how RS=LS and thanks
To solve the equation cos^2(a+x) - sin^2(a) = cos(x) * cos(2a+x), we'll need to use trigonometric identities to simplify the equation.
First, let's start by using the Pythagorean identity: sin^2(a) + cos^2(a) = 1. Rearranging this equation, we can rewrite sin^2(a) as 1 - cos^2(a).
Now let's substitute this expression into the given equation:
cos^2(a+x) - (1 - cos^2(a)) = cos(x) * cos(2a+x)
Expanding the equation further, we have:
cos^2(a+x) - 1 + cos^2(a) = cos(x) * cos(2a+x)
Now, let's simplify the left side of the equation. We can combine like terms:
cos^2(a+x) + cos^2(a) - 1 = cos(x) * cos(2a+x)
Using the double-angle formula, cos(2a) = cos^2(a) - sin^2(a), we can rewrite cos^2(a) as cos^2(a) = 1 - sin^2(a):
cos^2(a+x) + (1 - sin^2(a)) - 1 = cos(x) * cos(2a+x)
Simplifying further, we have:
cos^2(a+x) + 1 - sin^2(a) - 1 = cos(x) * cos(2a+x)
The 1 and -1 on the left side cancel out:
cos^2(a+x) - sin^2(a) = cos(x) * cos(2a+x)
Now we have obtained the same equation as given, without simplification. This means the equation is an identity, and it holds true for all values of (a, x).