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受欢迎的三角函数 >

tan^2(30)+cos^2(60)-sec^2(30)

解答

tan^{2} (3 0^{\circ}) + cos^{2} (6 0^{\circ}) - sec^{2} (3 0^{\circ})

解答

- \frac{3}{4}

+1

十进制

- 0.75

求解步骤

tan^{2} (3 0^{\circ}) + cos^{2} (6 0^{\circ}) - sec^{2} (3 0^{\circ})

使用以下普通恒等式:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (x)

周期表（周期为

18 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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

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:

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

sec (3 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= \frac{2 3}{3}

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

化简

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

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

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

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

使用指数法则:

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

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

(3)^{2} : 3

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

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

约分:

3

= \frac{1}{3}

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

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

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

使用指数法则:

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

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

使用指数法则:

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

(23)^{2} = 2^{2} (3)^{2}

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

(3)^{2} : 3

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

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

约分:

3

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

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

合并分式

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

使用法则

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

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

1 - 2^{2} = - 3

1 - 2^{2}

2^{2} = 4

= 1 - 4

数字相减:

1 - 4 = - 3

= - 3

= \frac{- 3}{3}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{3}

使用法则

\frac{a}{a} = 1

= - 1

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

2^{2} = 4

= - 1 + \frac{1}{4}

将项转换为分式:

1 = \frac{1 \cdot 4}{4}

= - \frac{1 \cdot 4}{4} + \frac{1}{4}

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 4 + 1}{4}

- 1 \cdot 4 + 1 = - 3

- 1 \cdot 4 + 1

数字相乘:

1 \cdot 4 = 4

= - 4 + 1

数字相加/相减:

- 4 + 1 = - 3

= - 3

= \frac{- 3}{4}

使用分式法则:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{4}

= - \frac{3}{4}

流行的例子

\frac{14}{cos ( 4 0 ^{\circ} )}

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cos (\frac{5 π}{4} - \frac{π}{3})

arctan(e)-arctan(1)

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sin (\frac{8}{13})