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受欢迎的三角函数 >

证明 cos(60)=1-2sin^2(30)

解答

证明

cos (6 0^{\circ}) = 1 - 2 sin^{2} (3 0^{\circ})

解答

真

求解步骤

cos (6 0^{\circ}) = 1 - 2 sin^{2} (3 0^{\circ})

调整左侧

cos (6 0^{\circ})

化简

= \frac{1}{2}

调整右侧

1 - 2 sin^{2} (3 0^{\circ})

化简

1 - 2 sin^{2} (3 0^{\circ}) : \frac{1}{2}

1 - 2 sin^{2} (3 0^{\circ})

2 sin^{2} (3 0^{\circ}) = \frac{1}{2}

2 sin^{2} (3 0^{\circ})

sin^{2} (3 0^{\circ}) = \frac{1}{2 ^{2}}

sin^{2} (3 0^{\circ})

化简

sin (3 0^{\circ}) : \frac{1}{2}

sin (3 0^{\circ})

使用以下普通恒等式:

sin (3 0^{\circ}) = \frac{1}{2}

sin (x)

周期表（周期为

36 0^{\circ} n

"）：

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{1}{2}

= (\frac{1}{2})^{2}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{1 ^{2}}{2 ^{2}}

使用法则

1^{a} = 1

1^{2} = 1

= \frac{1}{2 ^{2}}

= 2 \cdot \frac{1}{2 ^{2}}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{2}{2 ^{2}}

约分:

2

= \frac{1}{2}

= 1 - \frac{1}{2}

化简

1 - \frac{1}{2}

将项转换为分式:

1 = \frac{1 \cdot 2}{2}

= \frac{1 \cdot 2}{2} - \frac{1}{2}

因为分母相等，所以合并分式:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{1 \cdot 2 - 1}{2}

1 \cdot 2 - 1 = 1

1 \cdot 2 - 1

数字相乘:

1 \cdot 2 = 2

= 2 - 1

数字相减:

2 - 1 = 1

= 1

= \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

我们已展示，在两侧可以有相同的形式

\Rightarrow 真

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