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tan^2(45+(x/2))=4.137131

解答

tan^{2} (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

解答

x \in R 无解

求解步骤

tan^{2} (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

用替代法求解

tan^{2} (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

令

: tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = u

u^{2} = 4.137131

u^{2} = 4.137131 : u = 4.137131, u = - 4.137131

u^{2} = 4.137131

对于

x^{2} = f (a)

解为

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

u = 4.137131, u = - 4.137131

u = tan (4 5^{\circ} + (\frac{x}{2})^{\circ})

代回

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131, tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131, tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131 :

无解

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

使用反三角函数性质

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = 4.137131

的通解

tan (x) = a \Rightarrow x = arctan (a) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (4.137131) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (4.137131) + 18 0^{\circ} n

无解

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131 :

无解

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

使用反三角函数性质

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

tan (4 5^{\circ} + (\frac{x}{2})^{\circ}) = - 4.137131

的通解

tan (x) = - a \Rightarrow x = arctan (- a) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (- 4.137131) + 18 0^{\circ} n

4 5^{\circ} + (\frac{x}{2})^{\circ} = arctan (- 4.137131) + 18 0^{\circ} n

无解

合并所有解

x \in R 无解

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