The value of expression frac{{2(sin {1^o | vedclass

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Question

Numerator $=2\left[\left(\sin 1^{\circ}+\sin 89^{\circ}\right)+\right.$

$\left.\left(\sin 2^{\circ}+\sin 88^{\circ}\right)+\ldots \ldots+\left(\sin

Vedclass · Accepted Answer

$\sqrt 2$

Vedclass · Answer

Numerator $=2\left[\left(\sin 1^{\circ}+\sin 89^{\circ}ight)+ight.$

$\left.\left(\sin 2^{\circ}+\sin 88^{\circ}ight)+\ldots \ldots+\left(\sin 44^{\circ}+\sin 46^{\circ}ight)+\sin 45^{\circ}ight]$

$\Rightarrow \frac{	ext { Numerator }}{	ext { Denomin ator }}$

$=2\left[\sin 45^{\circ}\left\{2\left(\cos 44^{\circ}+\cos 43^{\circ}+\ldots+\cos 1^{\circ}ight)+1ight\}ight]$

$=2 \sin 45^{\circ}=\sqrt{2}$

The value of expression $\frac{{2(\sin {1^o} + \sin {2^o} + \sin {3^o} + ..... + \sin {{89}^o})}}{{2(\cos {1^o} + \cos {2^o} + .... + \cos {{44}^o}) + 1}}$ equals

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