Question

For which inverse functions are negative signs especially important?

Options

• \[\cos^{-1}x\], \[\cot^{-1}x\], and \[\operatorname{cosec}^{-1}x\]

• \[\tan^{-1}x\], \[\cot^{-1}x\], and \[\sec^{-1}x\]

• \[\sin^{-1}x\], \[\cos^{-1}x\], and \[\tan^{-1}x\]

• \[\sin^{-1}x\], \[\tan^{-1}x\], and \[\sec^{-1}x\]

Answer 1

Negative signs occur in the derivatives of \[\cos^{-1}x\], \[\cot^{-1}x\], and \[\operatorname{cosec}^{-1}x\]. Omitting these signs changes the derivative.