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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
0 votes

Find $\cos 55^{\large\circ}+\cos 65^{\large \circ}+\cos 175^{\large\circ}$

$(a)\;0\qquad(b)\;1\qquad(c)\;2\qquad(d)\;3$

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1 Answer

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$2\cos\large\frac{55^{\large\circ}+65^{\large\circ}}{2}$$\cos\large\frac{55^{\large\circ}-65^{\large\circ}}{2}$$+\cos175^{\large\circ}$
$\Rightarrow 2\cos 60^{\large\circ}\cos(-5)^{\large\circ}+\cos 175^{\large\circ}$
$\Rightarrow 2\times\large\frac{1}{2}.$$\cos 5^{\large\circ}+\cos(180^{\large\circ}-5^{\large\circ})$
$\Rightarrow \cos 5^{\large\circ}-\cos 5^{\large\circ}$
$\Rightarrow 0$
Hence (a) is the correct answer.
answered Oct 9, 2013 by sreemathi.v
 

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