What is the value of cos15° - cos165°?
A. $$\frac{{\sqrt 3 }}{{\sqrt 2 }}$$
B. $$\frac{2}{{\sqrt 3 - 1}}$$
C. $$\frac{{\sqrt 3 + 1}}{{\sqrt 2 }}$$
D. $$\frac{{\sqrt 3 + 1}}{2}$$
Answer: Option C
Solution (By Examveda Team)
\[\begin{array}{l} \cos {15^ \circ } - \cos {165^ \circ }\\ = \cos {15^ \circ } - \cos \left( {{{180}^ \circ } - {{15}^ \circ }} \right)\\ = \cos {15^ \circ } + \cos {15^ \circ }\\ = 2\cos {15^ \circ }\\ = 2\left( {\frac{{\sqrt 3 + 1}}{{2\sqrt 2 }}} \right)\\ = \frac{{\sqrt 3 + 1}}{{\sqrt 2 }}\\ {\bf{Note:}}\\ \left[ \begin{array}{l} \cos {15^ \circ } = \cos \left( {{{45}^ \circ } - {{30}^ \circ }} \right)\\ = \cos {45^ \circ }\cos {30^ \circ } + \sin {45^ \circ }\sin {30^ \circ }\\ = \frac{1}{{\sqrt 2 }} \times \frac{{\sqrt 3 }}{2} + \frac{1}{{\sqrt 2 }} \times \frac{1}{2}\\ = \frac{{\sqrt 3 + 1}}{{2\sqrt 2 }} \end{array} \right] \end{array}\]This Question Belongs to Arithmetic Ability >> Trigonometry
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