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受欢迎的三角函数 >

cos(2x)-sin^2(x)=1

解答

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

解答

x = 2 πn, x = π + 2 πn

+1

度数

x = 0^{\circ} + 36 0^{\circ} n, x = 18 0^{\circ} + 36 0^{\circ} n

求解步骤

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

两边减去

1

cos (2 x) - sin^{2} (x) - 1 = 0

使用三角恒等式改写

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

使用倍角公式:

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

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

化简

- 1 + 1 - 2 sin^{2} (x) - sin^{2} (x) : - 3 sin^{2} (x)

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

同类项相加:

- 2 sin^{2} (x) - sin^{2} (x) = - 3 sin^{2} (x)

= - 1 + 1 - 3 sin^{2} (x)

- 1 + 1 = 0

= - 3 sin^{2} (x)

= - 3 sin^{2} (x)

- 3 sin^{2} (x) = 0

两边除以

- 3

- 3 sin^{2} (x) = 0

两边除以

- 3

- 3 sin^{2} (x) = 0

两边除以

- 3

\frac{- 3 sin ^{2} ( x )}{- 3} = \frac{0}{- 3}

化简

sin^{2} (x) = 0

sin^{2} (x) = 0

使用法则

x^{n} = 0 \Rightarrow x = 0

sin (x) = 0

sin (x) = 0

的通解

sin (x)

周期表（周期为

2 πn

"）：

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

x = 0 + 2 πn, x = π + 2 πn

x = 0 + 2 πn, x = π + 2 πn

解

x = 0 + 2 πn : x = 2 πn

x = 0 + 2 πn

0 + 2 πn = 2 πn

x = 2 πn

x = 2 πn, x = π + 2 πn

作图

流行的例子

tan (a) = 2

sin(4x)cos(x)=cos(4x)sin(x)

sin (4 x) cos (x) = cos (4 x) sin (x)

cos(θ)-sqrt(cos(θ))=0

cos (θ) - cos (θ) = 0

2sin^2(x)=(csc^2(x))/2

2 sin^{2} (x) = \frac{csc ^{2} ( x )}{2}

5 cos (t) = 0