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  • Find dy/dx of each of the functions expressed in parametric form sin x = 2t/1+t^2

Find dy/dx of each of the functions expressed in parametric form in 

\sin \mathrm{x}=\frac{2 \mathrm{t}}{1+\mathrm{t}^{2}}, \tan \mathrm{y}=\frac{2 \mathrm{t}}{1-\mathrm{t}^{2}}

Answers (1)

We have given two parametric equation: \sin \mathrm{x}=\frac{2 \mathrm{t}}{1+\mathrm{t}^{2}}, \tan \mathrm{y}=\frac{2 \mathrm{t}}{1-\mathrm{t}^{2}}

Let us Assume t= tan θ

So, \frac{2 t}{1+t^{2}} \Rightarrow \frac{2 \tan \theta}{1+\tan ^{2} \theta} \\\Rightarrow \sin 2 \theta$ \\Therefore, \\$\sin x=\sin 2 \theta$ \\$x=2 \theta-(i)$ \\Also, \\tan $y=\tan 2 \theta$ \\$\mathrm{y}=2 \theta-\mathrm{c}(\mathrm{ii})$ \\From equation (i) and (ii) \\$y=x$ \\now, differentiate w.r.t x \\$\frac{\mathrm{dy}}{\mathrm{dx}}=1$ \\Hence, $\mathrm{dy} / \mathrm{dx}=1

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