frac{cos A}{1 - sin A} = | vedclass

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

Question

(D) We have $\frac{\cos A}{1 - \sin A}$.Multiply the numerator and denominator by $(1 + \sin A)$:$\frac{\cos A(1 + \sin A)}{(1 - \sin A)(1 + \sin A)}

Vedclass · Accepted Answer

$	an \left( \frac{\pi}{4} + \frac{A}{2} ight)$

Vedclass · Answer

(D) We have $\frac{\cos A}{1 - \sin A}$.Multiply the numerator and denominator by $(1 + \sin A)$:$\frac{\cos A(1 + \sin A)}{(1 - \sin A)(1 + \sin A)} = \frac{\cos A(1 + \sin A)}{1 - \sin^2 A} = \frac{\cos A(1 + \sin A)}{\cos^2 A} = \frac{1 + \sin A}{\cos A}$.Using half-angle identities $\sin A = 2 \sin \frac{A}{2} \cos \frac{A}{2}$ and $\cos A = \cos^2 \frac{A}{2} - \sin^2 \frac{A}{2}$:$= \frac{(\cos \frac{A}{2} + \sin \frac{A}{2})^2}{(\cos \frac{A}{2} - \sin \frac{A}{2})(\cos \frac{A}{2} + \sin \frac{A}{2})} = \frac{\cos \frac{A}{2} + \sin \frac{A}{2}}{\cos \frac{A}{2} - \sin \frac{A}{2}}$.Dividing numerator and denominator by $\cos \frac{A}{2}$:$= \frac{1 + 	an \frac{A}{2}}{1 - 	an \frac{A}{2}} = 	an \left( \frac{\pi}{4} + \frac{A}{2} ight)$.

$\frac{\cos A}{1 - \sin A} = $

Similar Questions

$\cos ^3 \theta + \cos ^3(120^{\circ} + \theta) + \cos ^3(\theta - 120^{\circ}) = $

If $\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32} = 2^m \operatorname{cosec} \frac{\pi}{n}$,then $m+n=$

The value of $\cos ^4 x$ is

The value of $x$ in $\left(0, \frac{\pi}{2}\right)$ satisfying the equation $(\sin x)(\cos x) = \frac{1}{4}$ is

If $\cosh x = \frac{5}{4}$,then $\tanh 3x =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module