The value of 1+cos⁡56∘+cos⁡58∘−cos⁡66∘is equal to

# The value of $1+\mathrm{cos}{56}^{\circ }+\mathrm{cos}{58}^{\circ }-\mathrm{cos}{66}^{\circ }$is equal to

1. A

$2\mathrm{cos}{28}^{\circ }\mathrm{cos}{29}^{\circ }\mathrm{cos}{33}^{\circ }$

2. B

$4\mathrm{cos}{28}^{\circ }\mathrm{cos}{29}^{\circ }\mathrm{sin}{33}^{\circ }$

3. C

$4\mathrm{cos}{28}^{\circ }\mathrm{cos}{29}^{\circ }\mathrm{cos}{33}^{\circ }$

4. D

$2\mathrm{cos}{28}^{\circ }\mathrm{cos}{29}^{\circ }\mathrm{sin}{33}^{\circ }$

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### Solution:

$\begin{array}{r}1+\mathrm{cos}{56}^{\circ }+\mathrm{cos}{58}^{\circ }-\mathrm{cos}{66}^{\circ }\\ =2{\mathrm{cos}}^{2}{28}^{\circ }+2\mathrm{sin}{62}^{\circ }\mathrm{sin}{4}^{\circ }\\ =2{\mathrm{cos}}^{2}{28}^{\circ }+2\mathrm{cos}{28}^{\circ }\mathrm{cos}{86}^{\circ }\\ =2\mathrm{cos}{28}^{\circ }\left(\mathrm{cos}{28}^{\circ }+\mathrm{cos}{86}^{\circ }\right)\\ =2\mathrm{cos}{28}^{\circ }\left(2\mathrm{cos}{57}^{\circ }\mathrm{cos}{29}^{\circ }\right)\\ =4\mathrm{cos}{28}^{\circ }\mathrm{cos}{29}^{\circ }\mathrm{cos}{33}^{\circ }\end{array}$

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