If f(x) = tan^{-1}left( frac{sin x}{1 + cos x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Given $f(x) = 	an^{-1}\left( \frac{\sin x}{1 + \cos x} ight)$.Using trigonometric identities,$\sin x = 2 \sin\left( \frac{x}{2} ight) \cos\le

Vedclass · Accepted Answer

$\frac{1}{2}$

Vedclass · Answer

(B) Given $f(x) = 	an^{-1}\left( \frac{\sin x}{1 + \cos x} ight)$.Using trigonometric identities,$\sin x = 2 \sin\left( \frac{x}{2} ight) \cos\left( \frac{x}{2} ight)$ and $1 + \cos x = 2 \cos^2\left( \frac{x}{2} ight)$.Substituting these into the function,we get $f(x) = 	an^{-1}\left( \frac{2 \sin(x/2) \cos(x/2)}{2 \cos^2(x/2)} ight) = 	an^{-1}\left( 	an\left( \frac{x}{2} ight) ight)$.Thus,$f(x) = \frac{x}{2}$.Differentiating with respect to $x$,we get $f'(x) = \frac{1}{2}$.Therefore,$f'\left( \frac{\pi}{3} ight) = \frac{1}{2}$.

If $f(x) = \tan^{-1}\left( \frac{\sin x}{1 + \cos x} \right)$,then $f'\left( \frac{\pi}{3} \right) = $

Similar Questions

If $f(x) = (x - x_0)g(x)$,where $g(x)$ is continuous at $x_0$,then $f'(x_0)$ is equal to

Let $f(x)$ be a differentiable function for all $x \in R$ and $f(x+y)=f(x)+f(y)-3xy$. If $\lim _{h \rightarrow 0} \frac{f(h)}{h}=7$,then $f^{\prime}(x)=$

If $f'(x)$ is zero in the interval $(a, b)$,then in this interval it is

Find the derivative of the following function (it is to be understood that $a, b, c, d, p, q, r$ and $s$ are fixed non-zero constants and $m$ and $n$ are integers): $\frac{a+b \sin x}{c+d \cos x}$

Find the derivative: $\frac{d}{dx}[\cos((1 - x^2)^2)] = ?$

Vedclass Test Series

Exam Paper Generator

Online Exam Module