If A = frac{pi}{24},then frac{cos A + cos 3A | vedclass

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

Question

(A) Let $I = \frac{\cos A + \cos 3A + \cos 5A + \cos 7A}{\sin A + \sin 3A + \sin 5A + \sin 7A}$.Grouping the terms in the numerator and denominator:$I

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(A) Let $I = \frac{\cos A + \cos 3A + \cos 5A + \cos 7A}{\sin A + \sin 3A + \sin 5A + \sin 7A}$.Grouping the terms in the numerator and denominator:$I = \frac{(\cos 7A + \cos A) + (\cos 5A + \cos 3A)}{(\sin 7A + \sin A) + (\sin 5A + \sin 3A)}$.Using the sum-to-product formulas $\cos C + \cos D = 2\cos\frac{C+D}{2}\cos\frac{C-D}{2}$ and $\sin C + \sin D = 2\sin\frac{C+D}{2}\cos\frac{C-D}{2}$:$I = \frac{2\cos 4A \cos 3A + 2\cos 4A \cos A}{2\sin 4A \cos 3A + 2\sin 4A \cos A}$.Factoring out common terms:$I = \frac{2\cos 4A (\cos 3A + \cos A)}{2\sin 4A (\cos 3A + \cos A)}$.$I = \frac{\cos 4A}{\sin 4A} = \cot 4A$.Given $A = \frac{\pi}{24}$,then $4A = 4 	imes \frac{\pi}{24} = \frac{\pi}{6}$.$I = \cot\frac{\pi}{6} = \sqrt{3}$.

If $A = \frac{\pi}{24}$,then $\frac{\cos A + \cos 3A + \cos 5A + \cos 7A}{\sin A + \sin 3A + \sin 5A + \sin 7A} = $

Similar Questions

The value of $\cos ^{2} 75^{\circ}+\cos ^{2} 45^{\circ}+\cos ^{2} 15^{\circ}-\cos ^{2} 30^{\circ}-\cos ^{2} 60^{\circ}$ is

If $\sin \theta = \sin 15^{\circ} + \sin 45^{\circ}$,where $0^{\circ} < \theta < 180^{\circ}$,then $\theta =$ (in $^{\circ}$)

For $\theta \in \left(0, \frac{\pi}{2}\right)$,if $\tan 3\theta \cdot \tan 2\theta \cdot \tan \theta + \tan 2\theta + \tan \theta = 1$,then $\theta =$

$\frac{\sin(B + A) + \cos(B - A)}{\sin(B - A) + \cos(B + A)} = $

The value of $\cos 15^\circ - \sin 15^\circ$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module