化简 sqrt((3)^2+(-3tan(t))^2)

解答

化简

(3)^{2} + (- 3 tan (t))^{2}

3 sec^{2} (t)

求解步骤

3^{2} + (- 3 tan (t))^{2}

(- 3 tan (t))^{2} = 3^{2} tan^{2} (t)

= 3^{2} + 3^{2} tan^{2} (t)

分解

3^{2} + 3^{2} tan^{2} (t) : 9 (1 + tan^{2} (t))

= 9 (1 + tan^{2} (t))

使用根式运算法则:

n ab = n a n b,

假定

a \geq 0, b \geq 0

= 9 tan^{2} (t) + 1

9 = 3

= 3 tan^{2} (t) + 1

使用三角恒等式改写

= 3 sec^{2} (t)

s im pl i f y cos (\frac{π}{2} - 2 x)

s im pl i f y cos (- 2 nπ)

f (x) = cos (9 0^{\circ} + arccos (x))

s im pl i f y \frac{sin ( π + x )}{cos ( 2 π + x )}

s im pl i f y ln (1 - sin^{2} (x))