the rate of change of sine is n then the rate of change of tangent is?

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Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{According} \mathrm{to} \mathrm{question} \\ \frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{sint}\right)=\mathrm{n} \\ \frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{sint}\right)=\mathrm{cost} \\ \mathbf{cost}\mathbf{=}\mathbf{n} \\ \frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{cost}\right) \mathrm{is} \mathrm{rate} \mathrm{of} \mathrm{change} \mathrm{of} \mathrm{tangent} \\ \frac{\mathrm{d}}{\mathrm{dt}}\left(\mathrm{cost}\right)=-\mathrm{sint} \\ =\pm \sqrt{1-{\cos }^2\mathrm{t}} \left[\mathrm{sinA}=\pm \sqrt{1-{\cos }^2\mathrm{A}}\right] \\ =-\sqrt{1-{\mathrm{n}}^2} \mathrm{or} \sqrt{1-{\mathrm{n}}^2} \end{gathered}$$

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