化简 (1-sec(θ))^2-tan^2(θ)

解答

化简

(1 - sec (θ))^{2} - tan^{2} (θ)

- 2 sec (θ) + 2

求解步骤

(1 - sec (θ))^{2} - tan^{2} (θ)

展开

(1 - sec (θ))^{2} : 1 - 2 sec (θ) + sec^{2} (θ)

= 1 - 2 sec (θ) + sec^{2} (θ) - tan^{2} (θ)

使用毕达哥拉斯恒等式:

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

sec^{2} (x) - tan^{2} (x) = 1

= - 2 sec (θ) + 1 + 1

数字相加:

1 + 1 = 2

= - 2 sec (θ) + 2

s im pl i f y (1 + 2 x + 3)^{2}

e x p an d \frac{( x + 1 ) ^{2}}{16}

e x p an d \frac{3 ( 1 + 6 )}{5}

e x p an d 5 cos (t) (4 sin (t) - 9 tan (t))

e x p an d - sin (t) (t + sin (t))^{2}