frac{{tan A + sec A - 1}}{{tan A - sec A + 1} | vedclass

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

Question

(C) We know that $1 = \sec^2 A - 	an^2 A$. Substituting this in the numerator:$\frac{{	an A + \sec A - (\sec^2 A - 	an^2 A)}}{{	an A - \sec A + 1}

Vedclass · Accepted Answer

$\frac{{1 + \sin A}}{{\cos A}}$

Vedclass · Answer

(C) We know that $1 = \sec^2 A - 	an^2 A$. Substituting this in the numerator:$\frac{{	an A + \sec A - (\sec^2 A - 	an^2 A)}}{{	an A - \sec A + 1}}$$= \frac{{(	an A + \sec A) - (\sec A - 	an A)(\sec A + 	an A)}}{{	an A - \sec A + 1}}$$= \frac{{(	an A + \sec A)(1 - (\sec A - 	an A))}}{{	an A - \sec A + 1}}$$= \frac{{(	an A + \sec A)(1 - \sec A + 	an A)}}{{	an A - \sec A + 1}}$Since the term $(1 - \sec A + 	an A)$ is common in the numerator and denominator,they cancel out:$= 	an A + \sec A$$= \frac{{\sin A}}{{\cos A}} + \frac{1}{{\cos A}}$$= \frac{{1 + \sin A}}{{\cos A}}$Thus,the correct option is $C$.

$\frac{{\tan A + \sec A - 1}}{{\tan A - \sec A + 1}} = $

Similar Questions

If $p = \frac{2 \sin \theta}{1 + \cos \theta + \sin \theta}$ and $q = \frac{\cos \theta}{1 + \sin \theta}$,then

The value of $\cos 24^{\circ} + \cos 55^{\circ} + \cos 125^{\circ} + \cos 204^{\circ} + \cos 300^{\circ}$ is

Which one of the following is true?

$\cot (45^\circ + \theta ) \cot (45^\circ - \theta ) = $

If $0 < \theta < \pi$,then the minimum value of $3\sin \theta + \csc^3 \theta$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module