簡約 1/(1+tan^2(x))+1/(1+cot^2(x))

解

簡約

\frac{1}{1 + tan ^{2} ( x )} + \frac{1}{1 + cot ^{2} ( x )}

1

解答ステップ

\frac{1}{1 + tan ^{2} ( x )} + \frac{1}{1 + cot ^{2} ( x )}

\frac{1}{1 + tan ^{2} ( x )} = \frac{1}{sec ^{2} ( x )}

\frac{1}{1 + cot ^{2} ( x )} = \frac{1}{csc ^{2} ( x )}

= \frac{1}{sec ^{2} ( x )} + \frac{1}{csc ^{2} ( x )}

\frac{1}{sec ^{2} ( x )} = cos^{2} (x)

\frac{1}{csc ^{2} ( x )} = sin^{2} (x)

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

ピタゴラスの公式を使用する:

cos^{2} (x) + sin^{2} (x) = 1

= 1