Question

proof it!
cos(a+b).cos(a-b)=cos^2a - sin^2b

Answer 1

cos (x + y) = cos x * cos y - sin x * sin y

and

cos (x - y) = cos x * cos y + sin x * sin y

=>

cos (a + b) * cos (a - b) =

(cos a * cos b - sin a * sin b) * (cos a * cos b + sin a * sin b)


If x = cos a * cos b and y = sin a * sin b

then

(cos a * cos b - sin a * sin b) * (cos a * cos b + sin a * sin b) =

(x - y) * (x + y) = x² - y²

<=>


(cos a * cos b - sin a * sin b) * (cos a * cos b + sin a * sin b) =

(cos a * cos b)² - (sin a * sin b)² =

(cos² a * cos² b) - (sin² a * sin² b)


cos² b + sin² b = 1 ===> cos² b = 1 - sin² b

and

cos² a + sin² a = 1 ===> sin² a = 1 - cos² a

=>

(cos² a * cos² b) - (sin² a * sin² b) =

(cos² a * (1 - sin² b)) - ((1 - cos² a) * sin² b) =

cos² a - cos² a * sin² b - sin² b + cos² a * sin² b =

cos² a - sin² b
...

Answer 2

thanks .
thank very much

Answer 3

welcome...

Answer 4

well.. i thought i made a mistake..