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

解

簡約

\frac{sin ^{2} ( x ) - cos ^{2} ( x )}{sin ( x ) - cos ( x )}

sin (x) + cos (x)

解答ステップ

\frac{sin ^{2} ( x ) - cos ^{2} ( x )}{sin ( x ) - cos ( x )}

2乗の差の公式を適用する:

x^{2} - y^{2} = (x + y) (x - y)

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

= \frac{( sin ( x ) + cos ( x ) ) ( sin ( x ) - cos ( x ) )}{sin ( x ) - cos ( x )}

共通因数を約分する:

sin (x) - cos (x)

= sin (x) + cos (x)