Question

If y = tanθ, then dy/dθ at θ = π/4 will be

Answer 1

$\textbf{Given:}$

$y=tan\theta$

$\textbf{To find:}$

$\dfrac{dy}{d\theta}\;\text{at}\,\theta=\frac{\pi}{4}$

$\textbf{Solution:}$

$\text{Consider,}$

$y=tan\theta$

$\text{Differentiate with respect to \theta }$

$\dfrac{dy}{d\theta}=sec^2\theta$

$\text{Now,}$

$(\dfrac{dy}{d\theta})_{\theta=\frac{\pi}{4}}=sec^2(\frac{\pi}{4})$

$(\dfrac{dy}{d\theta})_{\theta=\frac{\pi}{4}}=(\sqrt{2})^2$

$(\dfrac{dy}{d\theta})_{\theta=\frac{\pi}{4}}=2$

$\therefore\bf\,(\dfrac{dy}{d\theta})_{\theta=\frac{\pi}{4}}=2$

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Answer 2

this question requires high level thinking so firstly make a trigonometry table and fill the values in it and then put the value of second at 45 degree and square it you will get the answe