If tan theta = frac{p}{q}, then frac{p sin th | vedclass

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(B) Given $	an 	heta = \frac{\sin 	heta}{\cos 	heta} = \frac{p}{q}$.Divide the numerator and the denominator of the expression $\frac{p \sin 	het

Vedclass · Accepted Answer

$\frac{p^2 - q^2}{p^2 + q^2}$

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(B) Given $	an 	heta = \frac{\sin 	heta}{\cos 	heta} = \frac{p}{q}$.Divide the numerator and the denominator of the expression $\frac{p \sin 	heta - q \cos 	heta}{p \sin 	heta + q \cos 	heta}$ by $\cos 	heta$:$= \frac{p \frac{\sin 	heta}{\cos 	heta} - q}{p \frac{\sin 	heta}{\cos 	heta} + q}$Substitute $\frac{\sin 	heta}{\cos 	heta} = \frac{p}{q}$:$= \frac{p(\frac{p}{q}) - q}{p(\frac{p}{q}) + q} = \frac{\frac{p^2}{q} - q}{\frac{p^2}{q} + q}$$= \frac{\frac{p^2 - q^2}{q}}{\frac{p^2 + q^2}{q}} = \frac{p^2 - q^2}{p^2 + q^2}$.

If $\tan \theta = \frac{p}{q},$ then $\frac{p \sin \theta - q \cos \theta}{p \sin \theta + q \cos \theta} = $

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