If cot theta = frac{a}{b},then frac{cos theta | vedclass

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Question

(D) Given $\cot 	heta = \frac{a}{b}$.We know that $\cot 	heta = \frac{\cos 	heta}{\sin 	heta}$,so $\frac{\cos 	heta}{\sin 	heta} = \frac{a}{b}$.

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$\frac{a-b}{a+b}$

Vedclass · Answer

(D) Given $\cot 	heta = \frac{a}{b}$.We know that $\cot 	heta = \frac{\cos 	heta}{\sin 	heta}$,so $\frac{\cos 	heta}{\sin 	heta} = \frac{a}{b}$.To evaluate $\frac{\cos 	heta - \sin 	heta}{\cos 	heta + \sin 	heta}$,divide both the numerator and the denominator by $\sin 	heta$:$\frac{\frac{\cos 	heta}{\sin 	heta} - \frac{\sin 	heta}{\sin 	heta}}{\frac{\cos 	heta}{\sin 	heta} + \frac{\sin 	heta}{\sin 	heta}} = \frac{\cot 	heta - 1}{\cot 	heta + 1}$.Substituting $\cot 	heta = \frac{a}{b}$:$\frac{\frac{a}{b} - 1}{\frac{a}{b} + 1} = \frac{\frac{a-b}{b}}{\frac{a+b}{b}} = \frac{a-b}{a+b}$.

If $\cot \theta = \frac{a}{b}$,then $\frac{\cos \theta - \sin \theta}{\cos \theta + \sin \theta} = \ldots$

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