If frac{cos^4 alpha}{cos^2 beta} + frac{sin^4 | vedclass

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

Question

(B) Given: $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$.Let $\frac{\cos^2 \alpha}{\cos \beta} = \cos 	heta$ and $\fr

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) Given: $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$.Let $\frac{\cos^2 \alpha}{\cos \beta} = \cos 	heta$ and $\frac{\sin^2 \alpha}{\sin \beta} = \sin 	heta$.Then $\cos^2 \alpha = \cos \beta \cos 	heta$ and $\sin^2 \alpha = \sin \beta \sin 	heta$.Adding these,$\cos^2 \alpha + \sin^2 \alpha = \cos \beta \cos 	heta + \sin \beta \sin 	heta = \cos(\beta - 	heta) = 1$.This implies $\beta = 	heta + 2n\pi$,so $\cos \beta = \cos 	heta$ and $\sin \beta = \sin 	heta$.Substituting back,$\cos^2 \alpha = \cos^2 \beta$ and $\sin^2 \alpha = \sin^2 \beta$.Therefore,$\frac{\cos^4 \beta}{\cos^2 \alpha} + \frac{\sin^4 \beta}{\sin^2 \alpha} = \frac{\cos^4 \beta}{\cos^2 \beta} + \frac{\sin^4 \beta}{\sin^2 \beta} = \cos^2 \beta + \sin^2 \beta = 1$.The greatest integer value of $1$ is $[1] = 1$.

If $\frac{\cos^4 \alpha}{\cos^2 \beta} + \frac{\sin^4 \alpha}{\sin^2 \beta} = 1$,then the value of $\left[ \frac{\cos^4 \beta}{\cos^2 \alpha} + \frac{\sin^4 \beta}{\sin^2 \alpha} \right]$ is (where $[.]$ denotes the greatest integer function).

Similar Questions

The value of $\sin 10^\circ + \sin 20^\circ + \sin 30^\circ + ... + \sin 360^\circ$ is

$\tan 3A - \tan 2A - \tan A = $

If $\sin 5 \theta = \cos 20^{\circ}$ where $0^{\circ} < \theta < 90^{\circ}$,then the value of $\theta$ is (in degrees):

For any real values of $\theta$,$\sqrt{\frac{\sec \theta-1}{\sec \theta+1}} = ?$

Which of the following is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module