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受欢迎的三角函数 >

2cos^2(105)-1

解答

2 cos^{2} (10 5^{\circ}) - 1

解答

\frac{2 - 3}{2} - 1

+1

十进制

- 0.86602 \dots

求解步骤

2 cos^{2} (10 5^{\circ}) - 1

使用三角恒等式改写:

cos (10 5^{\circ}) = \frac{2 ( 1 - 3 )}{4}

cos (10 5^{\circ})

使用三角恒等式改写:

cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

cos (10 5^{\circ})

将

cos (10 5^{\circ})

写为

cos (6 0^{\circ} + 4 5^{\circ})

= cos (6 0^{\circ} + 4 5^{\circ})

使用角和恒等式:

cos (s + t) = cos (s) cos (t) - sin (s) sin (t)

= cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

= cos (6 0^{\circ}) cos (4 5^{\circ}) - sin (6 0^{\circ}) sin (4 5^{\circ})

使用以下普通恒等式:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{1}{2}

使用以下普通恒等式:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\circ})

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

= \frac{2}{2}

使用以下普通恒等式:

sin (6 0^{\circ}) = \frac{3}{2}

sin (6 0^{\circ})

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{3}{2}

使用以下普通恒等式:

sin (4 5^{\circ}) = \frac{2}{2}

sin (4 5^{\circ})

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{2}{2}

= \frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2}

化简

\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2} : \frac{2 ( 1 - 3 )}{4}

\frac{1}{2} \cdot \frac{2}{2} - \frac{3}{2} \cdot \frac{2}{2}

因式分解出通项

\frac{2}{2}

= \frac{2}{2} (\frac{1}{2} - \frac{3}{2})

\frac{1}{2} - \frac{3}{2} = \frac{1 - 3}{2}

\frac{1}{2} - \frac{3}{2}

使用法则

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

= \frac{1 - 3}{2}

= \frac{2}{2} \cdot \frac{1 - 3}{2}

分式相乘:

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

= \frac{( 1 - 3 ) 2}{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= \frac{2 ( 1 - 3 )}{4}

= \frac{2 ( 1 - 3 )}{4}

= 2 (\frac{2 ( 1 - 3 )}{4})^{2} - 1

化简

2 (\frac{2 ( 1 - 3 )}{4})^{2} - 1 : \frac{2 - 3}{2} - 1

2 (\frac{2 ( 1 - 3 )}{4})^{2} - 1

2 (\frac{2 ( 1 - 3 )}{4})^{2} = \frac{2 - 3}{2}

2 (\frac{2 ( 1 - 3 )}{4})^{2}

(\frac{2 ( 1 - 3 )}{4})^{2} = \frac{2 - 3}{2 ^{2}}

(\frac{2 ( 1 - 3 )}{4})^{2}

使用指数法则:

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

= \frac{( 2 ( 1 - 3 ) ) ^{2}}{4 ^{2}}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

(2 (1 - 3))^{2} = (2)^{2} (1 - 3)^{2}

= \frac{( 2 ) ^{2} ( 1 - 3 ) ^{2}}{4 ^{2}}

(2)^{2} : 2

使用根式运算法则:

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

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

使用指数法则:

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

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

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

\frac{1}{2} \cdot 2

分式相乘:

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

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

约分:

2

= 1

= 2

= \frac{2 ( 1 - 3 ) ^{2}}{4 ^{2}}

分解

4^{2} : 2^{4}

因式分解

4 = 2^{2}

= (2^{2})^{2}

化简

(2^{2})^{2} : 2^{4}

(2^{2})^{2}

使用指数法则:

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

= 2^{2 \cdot 2}

数字相乘:

2 \cdot 2 = 4

= 2^{4}

= 2^{4}

= \frac{2 ( 1 - 3 ) ^{2}}{2 ^{4}}

约分:

2

= \frac{( 1 - 3 ) ^{2}}{2 ^{3}}

(1 - 3)^{2} = 4 - 23

(1 - 3)^{2}

使用完全平方公式:

(a - b)^{2} = a^{2} - 2 ab + b^{2}

a = 1, b = 3

= 1^{2} - 2 \cdot 1 \cdot 3 + (3)^{2}

化简

1^{2} - 2 \cdot 1 \cdot 3 + (3)^{2} : 4 - 23

1^{2} - 2 \cdot 1 \cdot 3 + (3)^{2}

使用法则

1^{a} = 1

1^{2} = 1

= 1 - 2 \cdot 1 \cdot 3 + (3)^{2}

2 \cdot 1 \cdot 3 = 23

2 \cdot 1 \cdot 3

数字相乘:

2 \cdot 1 = 2

= 23

(3)^{2} = 3

(3)^{2}

使用根式运算法则:

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

= (3^{\frac{1}{2}})^{2}

使用指数法则:

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

= 3^{\frac{1}{2} \cdot 2}

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

\frac{1}{2} \cdot 2

分式相乘:

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

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

约分:

2

= 1

= 3

= 1 - 23 + 3

数字相加:

1 + 3 = 4

= 4 - 23

= 4 - 23

= \frac{4 - 2 3}{2 ^{3}}

分解

4 - 23 : 2 (2 - 3)

4 - 23

改写为

= 2 \cdot 2 - 23

因式分解出通项

2

= 2 (2 - 3)

= \frac{2 ( 2 - 3 )}{2 ^{3}}

约分:

2

= \frac{2 - 3}{2 ^{2}}

= 2 \cdot \frac{2 - 3}{2 ^{2}}

分式相乘:

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

= \frac{( 2 - 3 ) \cdot 2}{2 ^{2}}

约分:

2

= \frac{2 - 3}{2}

= \frac{2 - 3}{2} - 1

= \frac{2 - 3}{2} - 1

流行的例子

cos (10 8^{\circ})

6 sin (\frac{π}{4})

100 \cdot cos (3 0^{\circ})

sin (\frac{- 5 π}{3})

sin^2(270)-cos^2(270)+tan^2(60)

sin^{2} (27 0^{\circ}) - cos^{2} (27 0^{\circ}) + tan^{2} (6 0^{\circ})