The value of tan 67 frac{1}{2}^{circ} + cot 6 | vedclass

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(C) Let $x = 67 \frac{1}{2}^{\circ} = 67.5^{\circ}$. We need to evaluate $	an 67.5^{\circ} + \cot 67.5^{\circ}$.Using the identity $	an 	heta + \co

Vedclass · Accepted Answer

$2 \sqrt{2}$

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(C) Let $x = 67 \frac{1}{2}^{\circ} = 67.5^{\circ}$. We need to evaluate $	an 67.5^{\circ} + \cot 67.5^{\circ}$.Using the identity $	an 	heta + \cot 	heta = \frac{\sin 	heta}{\cos 	heta} + \frac{\cos 	heta}{\sin 	heta} = \frac{\sin^2 	heta + \cos^2 	heta}{\sin 	heta \cos 	heta} = \frac{1}{\sin 	heta \cos 	heta} = \frac{2}{\sin 2	heta}$.Here,$	heta = 67.5^{\circ}$,so $2	heta = 135^{\circ}$.Thus,$	an 67.5^{\circ} + \cot 67.5^{\circ} = \frac{2}{\sin 135^{\circ}}$.Since $\sin 135^{\circ} = \sin(180^{\circ} - 45^{\circ}) = \sin 45^{\circ} = \frac{1}{\sqrt{2}}$.Therefore,the value is $\frac{2}{1/\sqrt{2}} = 2 \sqrt{2}$.

The value of $\tan 67 \frac{1}{2}^{\circ} + \cot 67 \frac{1}{2}^{\circ}$ is

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