If sec theta = 1frac{1}{4},then tan frac{thet | vedclass

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

Question

(A) Given that $\sec 	heta = 1\frac{1}{4} = \frac{5}{4}$.We use the identity $\sec 	heta = \frac{1 + 	an^2(	heta/2)}{1 - 	an^2(	heta/2)}$.Substi

Vedclass · Accepted Answer

$\frac{1}{3}$

Vedclass · Answer

(A) Given that $\sec 	heta = 1\frac{1}{4} = \frac{5}{4}$.We use the identity $\sec 	heta = \frac{1 + 	an^2(	heta/2)}{1 - 	an^2(	heta/2)}$.Substituting the value of $\sec 	heta$:$\frac{5}{4} = \frac{1 + 	an^2(	heta/2)}{1 - 	an^2(	heta/2)}$.Cross-multiplying gives:$5(1 - 	an^2(	heta/2)) = 4(1 + 	an^2(	heta/2))$.$5 - 5	an^2(	heta/2) = 4 + 4	an^2(	heta/2)$.Rearranging the terms:$5 - 4 = 4	an^2(	heta/2) + 5	an^2(	heta/2)$.$1 = 9	an^2(	heta/2)$.$	an^2(	heta/2) = \frac{1}{9}$.Taking the square root,we get $	an(	heta/2) = \frac{1}{3}$ (assuming $	heta$ is in the first quadrant).

If $\sec \theta = 1\frac{1}{4}$,then $\tan \frac{\theta}{2} = $

Similar Questions

If $\sin x + \cos x = \frac{1}{5},$ then $\tan 2x$ is

The value of $\cos ^4 x$ is

If $\tanh(x) = \frac{1}{3}$,then $\tanh(3x)$ is

$\sqrt{\frac{1 - \sin A}{1 + \sin A}} = $

If $\cos \theta = \frac{1}{2}\left( x + \frac{1}{x} \right)$,then $\frac{1}{2}\left( x^2 + \frac{1}{x^2} \right) = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module