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Trigonometrical Equations
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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
A
$\sqrt 2$
B
$1/\sqrt 2$
C
$1/2$
D
$0$
Solution
Numerator $=2\left[\left(\sin 1^{\circ}+\sin 89^{\circ}\right)+\right.$
$\left.\left(\sin 2^{\circ}+\sin 88^{\circ}\right)+\ldots \ldots+\left(\sin 44^{\circ}+\sin 46^{\circ}\right)+\sin 45^{\circ}\right]$
$\Rightarrow \frac{\text { Numerator }}{\text { Denomin ator }}$
$=2\left[\sin 45^{\circ}\left\{2\left(\cos 44^{\circ}+\cos 43^{\circ}+\ldots+\cos 1^{\circ}\right)+1\right\}\right]$
$=2 \sin 45^{\circ}=\sqrt{2}$
Standard 11
Mathematics
