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

解

簡約

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

2

解答ステップ

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

(- cos (a) + sin (a))^{2} : cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a)

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

(cos (a) + sin (a))^{2} : cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a)

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

簡素化

cos^{2} (a) - 2 cos (a) sin (a) + sin^{2} (a) + cos^{2} (a) + 2 cos (a) sin (a) + sin^{2} (a) : 2 cos^{2} (a) + 2 sin^{2} (a)

= 2 cos^{2} (a) + 2 sin^{2} (a)

三角関数の公式を使用して書き換える

= 2