tan 1^circ tan 2^circ tan 3^circ tan 4^circ d | vedclass

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

Question

(A) We know that $	an(90^\circ - 	heta) = \cot 	heta$.Therefore,$	an 89^\circ = 	an(90^\circ - 1^\circ) = \cot 1^\circ$.Similarly,$	an 88^\circ

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) We know that $	an(90^\circ - 	heta) = \cot 	heta$.Therefore,$	an 89^\circ = 	an(90^\circ - 1^\circ) = \cot 1^\circ$.Similarly,$	an 88^\circ = \cot 2^\circ$,and so on.The expression can be written as: $(	an 1^\circ \cdot 	an 89^\circ) \cdot (	an 2^\circ \cdot 	an 88^\circ) \dots (	an 44^\circ \cdot 	an 46^\circ) \cdot 	an 45^\circ$.Since $	an 	heta \cdot \cot 	heta = 1$,each pair $(	an 	heta \cdot 	an(90^\circ - 	heta)) = 1$.There are $44$ such pairs,and $	an 45^\circ = 1$.Thus,the product is $1 	imes 1 	imes \dots 	imes 1 = 1$.

$\tan 1^\circ \tan 2^\circ \tan 3^\circ \tan 4^\circ \dots \tan 89^\circ = $

Similar Questions

If $\sin 5 \theta = \cos 20^{\circ}$ where $0^{\circ} < \theta < 90^{\circ}$,then the value of $\theta$ is (in degrees):

The exact value of $\cos^2 73^\circ + \cos^2 47^\circ + (\cos 73^\circ \cdot \cos 47^\circ)$ is

$\cos^2 48^\circ - \sin^2 12^\circ = $

If $0 < \theta < \pi$,then the minimum value of $3\sin \theta + \csc^3 \theta$ is

If $180^{\circ} < \theta < 270^{\circ},$ then the value of $\sqrt{4 \sin^{4} \theta + \sin^{2} 2\theta} + 4 \cos^{2} \left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module