Prove that frac{cos 4x + cos 3x + cos 2x}{sin | vedclass

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

Question

(N/A) $L.H.S. = \frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x}$$= \frac{(\cos 4x + \cos 2x) + \cos 3x}{(\sin 4x + \sin 2x) + \sin 3x}

Vedclass · Accepted Answer

Vedclass · Answer

(N/A) $L.H.S. = \frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x}$
$= \frac{(\cos 4x + \cos 2x) + \cos 3x}{(\sin 4x + \sin 2x) + \sin 3x}$
$= \frac{2 \cos(\frac{4x + 2x}{2}) \cos(\frac{4x - 2x}{2}) + \cos 3x}{2 \sin(\frac{4x + 2x}{2}) \cos(\frac{4x - 2x}{2}) + \sin 3x}$
Using the identities $\cos A + \cos B = 2 \cos(\frac{A+B}{2}) \cos(\frac{A-B}{2})$ and $\sin A + \sin B = 2 \sin(\frac{A+B}{2}) \cos(\frac{A-B}{2})$:
$= \frac{2 \cos 3x \cos x + \cos 3x}{2 \sin 3x \cos x + \sin 3x}$
$= \frac{\cos 3x(2 \cos x + 1)}{\sin 3x(2 \cos x + 1)}$
$= \frac{\cos 3x}{\sin 3x} = \cot 3x = R.H.S.$

Prove that $\frac{\cos 4x + \cos 3x + \cos 2x}{\sin 4x + \sin 3x + \sin 2x} = \cot 3x$.

Similar Questions

If $(1 + \tan \theta )(1 + \tan \phi ) = 2$,then $\theta + \phi = \dots ^\circ$

If $\tan \alpha = (1 + 2^{-x})^{-1}$ and $\tan \beta = (1 + 2^{x+1})^{-1}$,then $\alpha + \beta$ equals:

If $\tan \left( \frac{\pi }{4} + \theta \right) + \tan \left( \frac{\pi }{4} - \theta \right) = \lambda \sec 2\theta$,then $\lambda$ =

Prove that $\frac{\cos 9x - \cos 5x}{\sin 17x - \sin 3x} = -\frac{\sin 2x}{\cos 10x}$

Find the value of $\tan \frac{13 \pi}{12}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module