The value of cot 70^circ + 4cos 70^circ is | vedclass

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

Question

(B) Given expression: $\cot 70^\circ + 4\cos 70^\circ$$= \frac{\cos 70^\circ}{\sin 70^\circ} + 4\cos 70^\circ$$= \frac{\cos 70^\circ + 4\sin 70^\circ

Vedclass · Accepted Answer

$\sqrt{3}$

Vedclass · Answer

(B) Given expression: $\cot 70^\circ + 4\cos 70^\circ$$= \frac{\cos 70^\circ}{\sin 70^\circ} + 4\cos 70^\circ$$= \frac{\cos 70^\circ + 4\sin 70^\circ \cos 70^\circ}{\sin 70^\circ}$$= \frac{\cos 70^\circ + 2\sin 140^\circ}{\sin 70^\circ}$$= \frac{\cos 70^\circ + 2\sin(180^\circ - 40^\circ)}{\sin 70^\circ}$$= \frac{\cos 70^\circ + 2\sin 40^\circ}{\sin 70^\circ}$$= \frac{\sin 20^\circ + \sin 40^\circ + \sin 40^\circ}{\sin 70^\circ}$$= \frac{\sin 20^\circ + 2\sin 40^\circ}{\cos 20^\circ}$$= \frac{\sin 20^\circ + 2(2\sin 20^\circ \cos 20^\circ)}{\cos 20^\circ}$ (This approach is complex,let's use the standard identity approach:)$= \frac{\cos 70^\circ + 2\sin 140^\circ}{\sin 70^\circ} = \frac{\sin 20^\circ + 2\sin 40^\circ}{\cos 20^\circ} = \frac{\sin 20^\circ + \sin 40^\circ + \sin 40^\circ}{\cos 20^\circ} = \frac{2\sin 30^\circ \cos 10^\circ + \sin 40^\circ}{\cos 20^\circ}$$= \frac{\cos 10^\circ + \sin 40^\circ}{\cos 20^\circ} = \frac{\sin 80^\circ + \sin 40^\circ}{\cos 20^\circ} = \frac{2\sin 60^\circ \cos 20^\circ}{\cos 20^\circ} = 2 	imes \frac{\sqrt{3}}{2} = \sqrt{3}$.

The value of $\cot 70^\circ + 4\cos 70^\circ$ is

Similar Questions

$(m + 2)\sin \theta + (2m - 1)\cos \theta = 2m + 1$,then $\tan \theta$ is equal to:

The maximum value of $\cos^2 \left( \frac{\pi}{3} - x \right) - \cos^2 \left( \frac{\pi}{3} + x \right)$ is

If $x$ is real and $x+\frac{1}{x}=2 \cos \theta,$ then $\cos \theta=$

$\sqrt {2 + \sqrt {2 + 2\cos 4\theta } } = $

Given that $\cos \left( \frac{\alpha - \beta}{2} \right) = 2\cos \left( \frac{\alpha + \beta}{2} \right)$,then $\tan \frac{\alpha}{2} \tan \frac{\beta}{2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module