If tan theta = t, then tan 2theta + sec 2thet | vedclass

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

Question

(A) Given $	an 	heta = t.$We know the double angle formulas:$	an 2	heta = \frac{2	an 	heta}{1 - 	an^2 	heta} = \frac{2t}{1 - t^2}$$\cos 2	het

Vedclass · Accepted Answer

$\frac{1 + t}{1 - t}$

Vedclass · Answer

(A) Given $	an 	heta = t.$We know the double angle formulas:$	an 2	heta = \frac{2	an 	heta}{1 - 	an^2 	heta} = \frac{2t}{1 - t^2}$$\cos 2	heta = \frac{1 - 	an^2 	heta}{1 + 	an^2 	heta} = \frac{1 - t^2}{1 + t^2}$Therefore,$\sec 2	heta = \frac{1}{\cos 2	heta} = \frac{1 + t^2}{1 - t^2}$Now,$	an 2	heta + \sec 2	heta = \frac{2t}{1 - t^2} + \frac{1 + t^2}{1 - t^2}$$= \frac{2t + 1 + t^2}{1 - t^2} = \frac{(1 + t)^2}{(1 - t)(1 + t)}$$= \frac{1 + t}{1 - t}$.

If $\tan \theta = t,$ then $\tan 2\theta + \sec 2\theta = $

Similar Questions

If $\theta$ and $\phi$ are angles in the $1^{st}$ quadrant such that $\tan \theta = 1/7$ and $\sin \phi = 1/\sqrt{10}$. Then:

Let $A_0 A_1 A_2 A_3 A_4 A_5$ be a regular hexagon inscribed in a circle of unit radius. Then the product of the lengths of the line segments $A_0 A_1$,$A_0 A_2$,and $A_0 A_4$ is

$\frac{{\sin \theta }}{{1 - \cot \theta }} + \frac{{\cos \theta }}{{1 - \tan \theta }} = $

If $\sin A = \sin B$ and $\cos A = \cos B,$ then

If $\tan \theta = \frac{p}{q},$ then $\frac{p \sin \theta - q \cos \theta}{p \sin \theta + q \cos \theta} = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module