If 2 sec 2alpha = tan beta + cot beta,then on | vedclass

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

Question

(A) The given equation is $2 \sec 2\alpha = 	an \beta + \cot \beta$.We can rewrite the right side as:$	an \beta + \cot \beta = \frac{\sin \beta}{\co

Vedclass · Accepted Answer

$\frac{\pi}{4}$

Vedclass · Answer

(A) The given equation is $2 \sec 2\alpha = 	an \beta + \cot \beta$.We can rewrite the right side as:$	an \beta + \cot \beta = \frac{\sin \beta}{\cos \beta} + \frac{\cos \beta}{\sin \beta} = \frac{\sin^2 \beta + \cos^2 \beta}{\sin \beta \cos \beta} = \frac{1}{\sin \beta \cos \beta}$.Multiplying by $2$ in the numerator and denominator,we get $\frac{2}{2 \sin \beta \cos \beta} = \frac{2}{\sin 2\beta}$.So,the equation becomes $\frac{2}{\cos 2\alpha} = \frac{2}{\sin 2\beta}$.This implies $\cos 2\alpha = \sin 2\beta$.Using the identity $\sin 	heta = \cos(\frac{\pi}{2} - 	heta)$,we have $\cos 2\alpha = \cos(\frac{\pi}{2} - 2\beta)$.Therefore,$2\alpha = \frac{\pi}{2} - 2\beta$,which simplifies to $2\alpha + 2\beta = \frac{\pi}{2}$.Dividing by $2$,we get $\alpha + \beta = \frac{\pi}{4}$.

If $2 \sec 2\alpha = \tan \beta + \cot \beta$,then one of the values of $\alpha + \beta$ is

Similar Questions

If $\operatorname{cosec} \theta = \frac{p+q}{p-q}$,then $\cot \left(\frac{\pi}{4} + \frac{\theta}{2}\right)$ is equal to

If $\cosh 2x = 199$,then $\operatorname{coth} x =$

In a triangle $ABC$,$CD$ is the bisector of the angle $C$. If $\cos \frac{C}{2} = \frac{1}{3}$ and $CD = 6$,then the value of $\left( \frac{1}{a} + \frac{1}{b} \right)$ is equal to:

If $0 \leq \theta \leq 2 \pi$,$0 \leq \alpha \leq 2 \pi$ and $\sec ^{2018} \theta + \operatorname{cosec}^{2018} \alpha = 2$,then the value of $\cos ^{2020} \theta + \sin ^{2022} \alpha =$

The system of equations: $2x \cos^2 \theta + y \sin 2\theta - 2 \sin \theta = 0$,$x \sin 2\theta + 2y \sin^2 \theta = -2 \cos \theta$,and $x \sin \theta - y \cos \theta = 0$,for all values of $\theta$,can:

Vedclass Test Series

Exam Paper Generator

Online Exam Module