化简 (tan(x)-sin(x))^2+(1-cos(x))^2

解答

化简

(tan (x) - sin (x))^{2} + (1 - cos (x))^{2}

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

求解步骤

(tan (x) - sin (x))^{2} + (1 - cos (x))^{2}

展开

(tan (x) - sin (x))^{2} : tan^{2} (x) - 2 sin (x) tan (x) + sin^{2} (x)

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

展开

(1 - cos (x))^{2} : 1 - 2 cos (x) + cos^{2} (x)

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

使用毕达哥拉斯恒等式:

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

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

数字相加:

1 + 1 = 2

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

e x p an d sin (0)

e x p an d 3 cos (π (x - 1))

e x p an d \frac{( x ^{2} - 1 ) ^{2}}{4 x ^{2}}

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

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