\(VT=\cos^2a-2.\dfrac{1}{2}\left[\cos\left(a+b\right)+\cos\left(a-b\right)\right].\cos\left(a+b\right)+\cos^2\left(a+b\right)=\)
\(=\cos^2a-\cos^2\left(a+b\right)-\cos\left(a+b\right)\cos\left(a-b\right)+\cos^2\left(a+b\right)=\)
\(=\cos^2a-\dfrac{1}{2}\left(\cos2a+\cos2b\right)=\)
\(=\dfrac{2\cos^2a-\cos^2a+\sin^2a-1+2\sin^2b}{2}=\)
\(=\dfrac{\left(\cos^2a+\sin^2a\right)-1+2\sin^2b}{2}=\sin^2b=VP\)
cos2a - cos (a+b) (2 cosa . cosb - cos (a+b) = sin2b
Cos2a - ( cos a.cosb- sina .sinb)( 2 cosa .cosb - ( cosa .cosb - sina .sinb) = sin2b
cos2a - (cosa.cosb - sina.sinb) (cosa.cosb + sina .sinb) = sin2b
cos2a - ( cos2a . cos2b - sin2a .sin2b = sin2b ) .
1 - sin2a - ( 1 - sin2a ) ( 1 - sin2b) - sin2a .sin2b = sin2b
1 - sin2a - ( 1- sin2b - sin2a + sin2a .sin2b - sin2 a .sin2b = sin2b
1 - sin2a -1 + sin2 b + sin2a = sin2b
Sin2b = Sin2b điều đã CM
