If theta is a positive acute angle and tan 2t | vedclass

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(C) Given the equation $	an 2	heta \cdot 	an 3	heta = 1$.This can be rewritten as $	an 3	heta = \frac{1}{	an 2	heta} = \cot 2	heta$.Using the

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(C) Given the equation $	an 2	heta \cdot 	an 3	heta = 1$.This can be rewritten as $	an 3	heta = \frac{1}{	an 2	heta} = \cot 2	heta$.Using the identity $\cot A = 	an(90^{\circ} - A)$,we get $	an 3	heta = 	an(90^{\circ} - 2	heta)$.Equating the angles,$3	heta = 90^{\circ} - 2	heta$,which gives $5	heta = 90^{\circ}$,so $	heta = 18^{\circ}$.Now,we need to find the value of $(2 \cos^2 \frac{5	heta}{2} - 1)$.Substituting $	heta = 18^{\circ}$,we get $\frac{5	heta}{2} = \frac{5 	imes 18^{\circ}}{2} = 45^{\circ}$.Thus,the expression becomes $2 \cos^2 45^{\circ} - 1$.Since $\cos 45^{\circ} = \frac{1}{\sqrt{2}}$,then $\cos^2 45^{\circ} = \frac{1}{2}$.Therefore,$2 	imes (\frac{1}{2}) - 1 = 1 - 1 = 0$.

If $\theta$ is a positive acute angle and $\tan 2\theta \cdot \tan 3\theta = 1$,then the value of $(2 \cos^2 \frac{5\theta}{2} - 1)$ is:

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