zs

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

受欢迎的 >

(sin^2(x))/4 =(cos^2(x))/2

解答

\frac{sin ^{2} ( x )}{4} = \frac{cos ^{2} ( x )}{2}

解答

x = - 0.95531 \dots + πn, x = 0.95531 \dots + πn

+1

度数

x = - 54.73561 \dots^{\circ} + 18 0^{\circ} n, x = 54.73561 \dots^{\circ} + 18 0^{\circ} n

求解步骤

\frac{sin ^{2} ( x )}{4} = \frac{cos ^{2} ( x )}{2}

两边减去

\frac{cos ^{2} ( x )}{2}

\frac{sin ^{2} ( x )}{4} - \frac{cos ^{2} ( x )}{2} = 0

化简

\frac{sin ^{2} ( x )}{4} - \frac{cos ^{2} ( x )}{2} : \frac{sin ^{2} ( x ) - 2 cos ^{2} ( x )}{4}

\frac{sin ^{2} ( x )}{4} - \frac{cos ^{2} ( x )}{2}

4, 2

的最小公倍数:

4

4, 2

最小公倍数 (LCM)

4

质因数分解:

2 \cdot 2

4

4

除以

24 = 2 \cdot 2

= 2 \cdot 2

2

质因数分解:

2

2

2

是质数，因此无法因数分解

= 2

将每个因子乘以它在

4

或

2

中出现的最多次数

= 2 \cdot 2

数字相乘:

2 \cdot 2 = 4

= 4

根据最小公倍数调整分式

将每个分子乘以其分母转变为最小公倍数所要乘以的同一数值

4

对于

\frac{cos ^{2} ( x )}{2} :

将分母和分子乘以

2

\frac{cos ^{2} ( x )}{2} = \frac{cos ^{2} ( x ) \cdot 2}{2 \cdot 2} = \frac{cos ^{2} ( x ) \cdot 2}{4}

= \frac{sin ^{2} ( x )}{4} - \frac{cos ^{2} ( x ) \cdot 2}{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{sin ^{2} ( x ) - cos ^{2} ( x ) \cdot 2}{4}

\frac{sin ^{2} ( x ) - 2 cos ^{2} ( x )}{4} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

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

分解

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

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

将

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

改写为

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

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

使用根式运算法则:

a = (a)^{2}

2 = (2)^{2}

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

使用指数法则:

a^{m} b^{m} = (ab)^{m}

(2)^{2} cos^{2} (x) = (2 cos (x))^{2}

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

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

使用平方差公式:

x^{2} - y^{2} = (x + y) (x - y)

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

= (sin (x) + 2 cos (x)) (sin (x) - 2 cos (x))

(sin (x) + 2 cos (x)) (sin (x) - 2 cos (x)) = 0

分别求解每个部分

sin (x) + 2 cos (x) = 0 or sin (x) - 2 cos (x) = 0

sin (x) + 2 cos (x) = 0 : x = arctan (- 2) + πn

sin (x) + 2 cos (x) = 0

使用三角恒等式改写

sin (x) + 2 cos (x) = 0

在两边除以

cos (x), cos (x) \neq = 0

\frac{sin ( x ) + 2 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

化简

\frac{sin ( x )}{cos ( x )} + 2 = 0

使用基本三角恒等式:

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

tan (x) + 2 = 0

tan (x) + 2 = 0

将

2

到右边

tan (x) + 2 = 0

两边减去

2

tan (x) + 2 - 2 = 0 - 2

化简

tan (x) = - 2

tan (x) = - 2

使用反三角函数性质

tan (x) = - 2

tan (x) = - 2

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- 2) + πn

x = arctan (- 2) + πn

sin (x) - 2 cos (x) = 0 : x = arctan (2) + πn

sin (x) - 2 cos (x) = 0

使用三角恒等式改写

sin (x) - 2 cos (x) = 0

在两边除以

cos (x), cos (x) \neq = 0

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

化简

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

使用基本三角恒等式:

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

tan (x) - 2 = 0

tan (x) - 2 = 0

将

2

到右边

tan (x) - 2 = 0

两边加上

2

tan (x) - 2 + 2 = 0 + 2

化简

tan (x) = 2

tan (x) = 2

使用反三角函数性质

tan (x) = 2

tan (x) = 2

的通解

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (2) + πn

x = arctan (2) + πn

合并所有解

x = arctan (- 2) + πn, x = arctan (2) + πn

以小数形式表示解

x = - 0.95531 \dots + πn, x = 0.95531 \dots + πn

流行的例子

solvefor θ,2sin(θ)=tan(θ)求解

θ, 2 sin (θ) = tan (θ)

5cot^2(x)+8cot(x)+3=0

5 cot^{2} (x) + 8 cot (x) + 3 = 0

-2sin^2(x)-cos(x)+3=0

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

2tan^2(2x)-tan(2x)=3

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

sin (x) = \frac{15}{31}