The value of (tan 1^{circ} tan 2^{circ} tan 3 | vedclass

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(B) We have the expression: $P = 	an 1^{\circ} \cdot 	an 2^{\circ} \cdot 	an 3^{\circ} \ldots 	an 89^{\circ}$.Using the property $	an(90^{\circ}

Vedclass · Accepted Answer

$1$

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(B) We have the expression: $P = 	an 1^{\circ} \cdot 	an 2^{\circ} \cdot 	an 3^{\circ} \ldots 	an 89^{\circ}$.Using the property $	an(90^{\circ} - 	heta) = \cot 	heta$,we can write $	an 89^{\circ} = \cot 1^{\circ}$,$	an 88^{\circ} = \cot 2^{\circ}$,and so on.Since $\cot 	heta = \frac{1}{	an 	heta}$,we have $	an 89^{\circ} = \frac{1}{	an 1^{\circ}}$,$	an 88^{\circ} = \frac{1}{	an 2^{\circ}}$,etc.Substituting these into the expression:$P = (	an 1^{\circ} \cdot \cot 1^{\circ}) \cdot (	an 2^{\circ} \cdot \cot 2^{\circ}) \ldots (	an 44^{\circ} \cdot \cot 44^{\circ}) \cdot 	an 45^{\circ}$.Since $	an 	heta \cdot \cot 	heta = 1$ and $	an 45^{\circ} = 1$,the expression becomes:$P = 1 \cdot 1 \cdot 1 \ldots \cdot 1 = 1$.

The value of $(\tan 1^{\circ} \tan 2^{\circ} \tan 3^{\circ} \ldots \tan 89^{\circ})$ is

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Write 'True' or 'False' and justify your answer.
$\frac{\tan 47^{\circ}}{\cot 43^{\circ}}=1$

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