Trigonometric Identities Question 199
Question: The value of expression $ \frac{2(sin1^{o}+sin2^{o}+sin3^{o}+\cdot \cdot \cdot \cdot +\sin 89^{o})}{2(cos1^{o}+cos2^{o}+\cdot \cdot \cdot +cos44^{o})+1} $ Equals
Options:
A) $ \sqrt{2} $
B) $ 1/\sqrt{2} $
C) $ 1/2 $
D) 0
Show Answer
Answer:
Correct Answer: A
Solution:
[a] Numerator =2 $ 2[(sin1{}^\circ +\sin 89{}^\circ )+(sin2{}^\circ +sin88{}^\circ )+.. $ $ +(sin44{}^\circ +\sin 46{}^\circ )+sin45{}^\circ ] $
$ \Rightarrow ,\frac{Numerator}{Deno\min ator} $ $ =2[sin45{}^\circ {2(cos44{}^\circ +cos43{}^\circ +…cos1{}^\circ )+1}] $ $ =2\sin 45{}^\circ =\sqrt{2} $
BETA
