1+ 56^ + 58^ - 66^ = - Vidyadip

MCQ

$1+\cos 56^{\circ}+\cos 58^{\circ}-\cos 66^{\circ}=$

A
$2 \cos 28^{\circ} \cos 29^{\circ} \cos 33^{\circ}$
B
$4 \cos 28^{\circ} \cos 29^{\circ} \cos 33^{\circ}$
✓
$4 \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ}$
D
$2 \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ}$

✓

Answer

Correct option: C.

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

(C)
$1+\cos 56^{\circ}+\cos 58^{\circ}-\cos 66^{\circ}$
$=2 \cos ^2 28^{\circ}+2 \sin 62^{\circ} \sin 4^{\circ}$
$=2 \cos ^2 28^{\circ}+2 \cos 28^{\circ} \cos 86^{\circ}$$\ldots\left[\because \sin \left(90^{\circ}-\theta\right)=\cos \theta\right]$
$=2 \cos 28^{\circ}\left(\cos 28^{\circ}+\cos 86^{\circ}\right)$
$=2 \cos 28^{\circ} .2 \cos 57^{\circ} \cos 29^{\circ}$
$=4 \cos 28^{\circ} \cos 29^{\circ} \sin 33^{\circ}$$\ldots\left[\because \cos \left(90^{\circ}-\theta\right)=\sin \theta\right]$

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