展开 (sin^2(θ)+(1+cos(θ))^2)/(cos(θ)+1)

解答

展开

\frac{sin ^{2} ( θ ) + ( 1 + cos ( θ ) ) ^{2}}{cos ( θ ) + 1}

2

求解步骤

\frac{sin ^{2} ( θ ) + ( 1 + cos ( θ ) ) ^{2}}{cos ( θ ) + 1}

乘开

sin^{2} (θ) + (1 + cos (θ))^{2} : sin^{2} (θ) + 1 + 2 cos (θ) + cos^{2} (θ)

= \frac{sin ^{2} ( θ ) + 1 + 2 cos ( θ ) + cos ^{2} ( θ )}{cos ( θ ) + 1}

使用毕达哥拉斯恒等式:

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

= \frac{1 + 2 cos ( θ ) + 1}{1 + cos ( θ )}

1 + 2 cos (θ) + 1 = 2 cos (θ) + 2

= \frac{2 cos ( θ ) + 2}{1 + cos ( θ )}

分解

2 cos (θ) + 2 : 2 (cos (θ) + 1)

= \frac{2 ( cos ( θ ) + 1 )}{1 + cos ( θ )}

约分:

cos (θ) + 1

= 2

e x p an d \frac{2 x ^{2} + 6 x}{( x - 3 ) ( x + 1 )}

e x p an d (1 - x^{2})^{\frac{1}{2}} (1 + x^{3})

s im pl i f y - 2 (3 - 52)

e x p an d \frac{12}{s ( s + 10 ) ( s + 70 )}

s im pl i f y (\frac{x}{3} - 2) (\frac{x}{3} - 3)