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

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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

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