int frac{dx}{cos x sqrt{cos 2x}} = | vedclass

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

Question

(D) Let $I = \int \frac{dx}{\cos x \sqrt{\cos 2x}}$.Divide the numerator and denominator by $\cos x$ inside the square root or manipulate the expressi

Vedclass · Accepted Answer

$\sin^{-1}(	an x)+c$

Vedclass · Answer

(D) Let $I = \int \frac{dx}{\cos x \sqrt{\cos 2x}}$.Divide the numerator and denominator by $\cos x$ inside the square root or manipulate the expression as follows:$I = \int \frac{dx}{\cos x \sqrt{\cos^2 x - \sin^2 x}} = \int \frac{dx}{\cos x \cdot \cos x \sqrt{1 - 	an^2 x}} = \int \frac{\sec^2 x}{\sqrt{1 - 	an^2 x}} dx$.Let $	an x = t$,then $\sec^2 x \, dx = dt$.Substituting these into the integral,we get:$I = \int \frac{dt}{\sqrt{1 - t^2}} = \sin^{-1}(t) + c$.Replacing $t$ with $	an x$,we get:$I = \sin^{-1}(	an x) + c$.

$\int \frac{dx}{\cos x \sqrt{\cos 2x}} =$

Similar Questions

The simplest formula of a compound containing $50\%$ of element $X$ (atomic mass $10$) and $50\%$ of element $Y$ (atomic mass $20$) is

The resultant gate and its Boolean expression in the given circuit is

If $\theta$ lies in the first quadrant and $5 \tan \theta = 4$,then $\frac{5 \sin \theta - 3 \cos \theta}{\sin \theta + 2 \cos \theta}$ is equal to

The species having tetrahedral shape is

$75 \ mL$ of $0.2 \ M \ HCl$ is mixed with $25 \ mL$ of $1 \ M \ HCl$. To this solution,$300 \ mL$ of distilled water is added. What is the $pH$ of the resultant solution?

Vedclass Test Series

Exam Paper Generator

Online Exam Module