sin(5X)*cos(5X)=1

解答

sin (5 X) \cdot cos (5 X) = 1

X \in R 无解

求解步骤

sin (5 X) cos (5 X) = 1

使用三角恒等式改写

sin (5 X) cos (5 X)

使用倍角公式:

2 sin (x) cos (x) = sin (2 x)

sin (x) cos (x) = \frac{sin ( 2 x )}{2}

= \frac{sin ( 2 \cdot 5 X )}{2}

\frac{sin ( 2 \cdot 5 X )}{2} = 1

在两边乘以

2

\frac{sin ( 2 \cdot 5 X )}{2} = 1

在两边乘以

2

\frac{2 sin ( 2 \cdot 5 X )}{2} = 1 \cdot 2

化简

sin (2 \cdot 5 X) = 2

sin (2 \cdot 5 X) = 2

- 1 \leq sin (x) \leq 1

X \in R 无解

100 + 60 sin (\frac{7 π}{3} x) = 100

sin^{2} (a) = 3 cos^{2} (a)

3 cot (x) + 3 = 0

3 cos (x) + \frac{9}{2} = 5 + 4 cos (x)

sec (2 x) + 2 = 0