A) 2
B) 1
C) \[1/2\]
D) 0
Correct Answer: D
Solution :
\[\cos 20{}^\circ +\cos 100{}^\circ +\cos 140{}^\circ \] \[=(\cos \,140{}^\circ +\cos 20{}^\circ )+\cos 100{}^\circ \] \[=2\cos \left( \frac{160{}^\circ }{2} \right).\cos \left( \frac{120{}^\circ }{2} \right)+\cos 100{}^\circ \] \[=2.80{}^\circ .\frac{1}{2}+\cos 100{}^\circ \] \[=2\cos \left( \frac{180{}^\circ }{2} \right).\cos \left( \frac{20{}^\circ }{2} \right)\] \[=2\cos 90{}^\circ .\,\cos 10{}^\circ \] \[=2\times 10\times \cos 10{}^\circ =0\]
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