簡約 2(sin(x)cos(x)-cos^2(x))+cos(2x)+sin(2x)

解

簡約

2 (sin (x) cos (x) - cos^{2} (x)) + cos (2 x) + sin (2 x)

cos (2 x) + 2 sin (2 x) - 2 cos^{2} (x)

解答ステップ

2 (sin (x) cos (x) - cos^{2} (x)) + cos (2 x) + sin (2 x)

拡張

2 (sin (x) cos (x) - cos^{2} (x)) : 2 cos (x) sin (x) - 2 cos^{2} (x)

= 2 cos (x) sin (x) - 2 cos^{2} (x) + cos (2 x) + sin (2 x)

2倍角の公式を使用:

2 sin (x) cos (x) = sin (2 x)

= cos (2 x) + sin (2 x) + sin (2 x) - 2 cos^{2} (x)

類似した元を足す:

sin (2 x) + sin (2 x) = 2 sin (2 x)

= cos (2 x) + 2 sin (2 x) - 2 cos^{2} (x)