यदि m tan (theta - 30^circ) = n tan (theta + | vedclass

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(A) दिया गया है,$m 	an (	heta - 30^\circ) = n 	an (	heta + 120^\circ)$.$\frac{m}{n} = \frac{	an (	heta + 120^\circ)}{	an (	heta - 30^\circ)}$.

Vedclass · Accepted Answer

$2 \cos 2	heta$

Vedclass · Answer

(A) दिया गया है,$m 	an (	heta - 30^\circ) = n 	an (	heta + 120^\circ)$.$\frac{m}{n} = \frac{	an (	heta + 120^\circ)}{	an (	heta - 30^\circ)}$.योगानुपात और अंतरानुपात (componendo and dividendo) का उपयोग करने पर:$\frac{m + n}{m - n} = \frac{	an (	heta + 120^\circ) + 	an (	heta - 30^\circ)}{	an (	heta + 120^\circ) - 	an (	heta - 30^\circ)}$.$\frac{m + n}{m - n} = \frac{\sin((	heta + 120^\circ) + (	heta - 30^\circ))}{\sin((	heta + 120^\circ) - (	heta - 30^\circ))} = \frac{\sin(2	heta + 90^\circ)}{\sin(150^\circ)}$.चूँकि $\sin(2	heta + 90^\circ) = \cos 2	heta$ और $\sin(150^\circ) = \frac{1}{2}$ है:$\frac{m + n}{m - n} = \frac{\cos 2	heta}{1/2} = 2 \cos 2	heta$.

यदि $m \tan (\theta - 30^\circ) = n \tan (\theta + 120^\circ)$ है,तो $\frac{m + n}{m - n} = $

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