Q. The value of$\ 1 + \cos{56{^\circ} + \cos{58{^\circ} - \cos{66{^\circ}\ }}}$is equal to
A) $2\cos{28{^\circ}\cos{29{^\circ}\cos{33{^\circ}}}}$
B) $4\cos{28{^\circ}\cos{29{^\circ}\sin{33{^\circ}}}}$
C) $4\cos{28{^\circ}\cos{29{^\circ}\cos{33{^\circ}}}}$
D) $2\cos{28{^\circ}\cos{29{^\circ}\sin{33{^\circ}}}}$
Explanation
(b)
$1 + \cos{56{^\circ} + \cos{58{^\circ} - \cos{66{^\circ}}}}$
$= 2\cos^{2}{28{^\circ} + 2\sin{62{^\circ}\sin{4{^\circ}}}}$
$= 2\cos^{2}{28{^\circ} + 2\cos{28{^\circ}\cos{86{^\circ}}}}$
$= 2\cos{28{^\circ}(\cos{28{^\circ} + \cos{86{^\circ})}}}$
$= 2\cos{28{^\circ}(2\cos{57{^\circ}\cos{29{^\circ})}}}$
$= 4\cos{28{^\circ}\cos{29{^\circ}\sin{33{^\circ}}}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.