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受欢迎的三角函数 >

(1+(tan^2(a))/1+cot^2(a))=tan^2(a)

解答

(1 + \frac{tan ^{2} ( a )}{1} + cot^{2} (a)) = tan^{2} (a)

解答

a \in R 无解

求解步骤

(1 + \frac{tan ^{2} ( a )}{1} + cot^{2} (a)) = tan^{2} (a)

两边减去

tan^{2} (a)

cot^{2} (a) + 1 = 0

用替代法求解

cot^{2} (a) + 1 = 0

令

: cot (a) = u

u^{2} + 1 = 0

u^{2} + 1 = 0 : u = i, u = - i

u^{2} + 1 = 0

将

1

到右边

u^{2} + 1 = 0

两边减去

1

u^{2} + 1 - 1 = 0 - 1

化简

u^{2} = - 1

u^{2} = - 1

对于

x^{2} = f (a)

解为

x = f (a), - f (a)

u = - 1, u = - - 1

化简

- 1 : i

- 1

使用虚数运算法则:

- 1 = i

= i

化简

- - 1 : - i

- - 1

使用虚数运算法则:

- 1 = i

= - i

u = i, u = - i

u = cot (a)

代回

cot (a) = i, cot (a) = - i

cot (a) = i, cot (a) = - i

cot (a) = i :

无解

cot (a) = i

无解

cot (a) = - i :

无解

cot (a) = - i

无解

合并所有解

a \in R 无解

作图

流行的例子

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

4cos^2(x)-11cos(x)+7=0

4 cos^{2} (x) - 11 cos (x) + 7 = 0

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(1+cos^2(x))/(sin^2(x))= 1/(sin^2(x))

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