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第4章:坐标变换
高三数学 | 高级数学
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2.4 Inverse Trigonometric Function Equations 反三角函数方程式


Solve the following equations
截下列各方程式

1. tan^{-1}x = cot^{-1}x

Answer :
1
2. tan^{-1}x + tan^{-1}(1 - x) = 2tan^{-1}\sqrt{x-x^2}
Answer :
\frac{1}{2}
3. sin^{-1}x = cos^{-1} (1 - x)
Answer :
0, 1
4. sin^{-1}x + sin^{-1}2x = \frac{\pi}{3}
Answer :
\sqrt{\frac{3}{28}}
5. 2sin^{-1}x = sin^{-1}2x - cos^{-1}x
Answer :
无解
6. {tan}^{-1}{x}+2{cot}^{-1}{x}=\frac{3\pi}{4}
Answer :
1
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