簡約 1/(sin^2(x)+tan^2(x)+cos^2(x))+3cos^2(x)

解

簡約

\frac{1}{sin ^{2} ( x ) + tan ^{2} ( x ) + cos ^{2} ( x )} + 3 cos^{2} (x)

4 cos^{2} (x)

解答ステップ

\frac{1}{sin ^{2} ( x ) + tan ^{2} ( x ) + cos ^{2} ( x )} + 3 cos^{2} (x)

簡素化

sin^{2} (x) + tan^{2} (x) + cos^{2} (x) : sec^{2} (x)

= \frac{1}{sec ^{2} ( x )} + 3 cos^{2} (x)

簡素化

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

= cos^{2} (x) + 3 cos^{2} (x)

類似した元を足す:

cos^{2} (x) + 3 cos^{2} (x) = 4 cos^{2} (x)

= 4 cos^{2} (x)