Question

Which inverse functions have denominator \[\sqrt{1-x^2}\] in their derivatives?

Options

• \[\sin^{-1}x\] and \[\cos^{-1}x\]

• \[\tan^{-1}x\] and \[\cot^{-1}x\]

• \[\sec^{-1}x\] and \[\operatorname{cosec}^{-1}x\]

• \[\sin^{-1}x\] and \[\tan^{-1}x\]

Answer 1

Both \[\sin^{-1}x\] and \[\cos^{-1}x\] have denominator \[\sqrt{1-x^2}\]. Their derivatives differ in sign.