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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) We are given the expression: $	an 1^{\circ} 	an 2^{\circ} 	an 3^{\circ} \ldots 	an 89^{\circ}$.Using the property $	an(90^{\circ} - 	heta) =

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(B) We are given the expression: $	an 1^{\circ} 	an 2^{\circ} 	an 3^{\circ} \ldots 	an 89^{\circ}$.Using the property $	an(90^{\circ} - 	heta) = \cot 	heta$,we can rewrite the terms from $46^{\circ}$ to $89^{\circ}$ as:$	an 89^{\circ} = 	an(90^{\circ} - 1^{\circ}) = \cot 1^{\circ}$$	an 88^{\circ} = 	an(90^{\circ} - 2^{\circ}) = \cot 2^{\circ}$$\dots$$	an 46^{\circ} = 	an(90^{\circ} - 44^{\circ}) = \cot 44^{\circ}$.Substituting these into the expression:$= (	an 1^{\circ} \cot 1^{\circ}) 	imes (	an 2^{\circ} \cot 2^{\circ}) 	imes \dots 	imes (	an 44^{\circ} \cot 44^{\circ}) 	imes 	an 45^{\circ}$.Since $	an 	heta \cot 	heta = 1$ and $	an 45^{\circ} = 1$,the expression becomes:$= 1 	imes 1 	imes \dots 	imes 1 	imes 1 = 1$.

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

Similar Questions

If $\tan \theta = - \frac{1}{\sqrt{10}}$ and $\theta$ lies in the fourth quadrant,then $\cos \theta = $

$A$ circular wire of diameter $10 \, cm$ is cut and placed along the circumference of a circle of diameter $1 \, m$. The angle subtended by the wire at the centre of the circle is equal to:

Suppose $ABC$ is a triangle and $D, E$ are points on the sides $AB$ and $AC$ respectively. If $AD : AB = 3 : 5$ and $AE : AC = 2 : 3$,then the ratio of the areas of the triangles $ABC$ and $ADE$ lies in the interval.

Find the value of the trigonometric function $\tan \frac{19 \pi}{3}$.

Find the radian measure corresponding to the following degree measure: $520^{\circ}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module