(45^ +A ) (45^ -A )= - Vidyadip

MCQ

$\sin \left(45^{\circ}+A\right) \sin \left(45^{\circ}-A\right)=$

A
$\cos A$
✓
$\frac{1}{2} \cos 2 A$
C
$\cos 2 A$
D
$\frac{1}{2} \cos A$

✓

Answer

Correct option: B.

$\frac{1}{2} \cos 2 A$

(B)
$\sin \left(45^{\circ}+ A \right) \sin \left(45^{\circ}- A \right)$
$=\frac{1}{2}\left[2 \sin \left(45^{\circ}+ A \right) \sin \left(45^{\circ}- A \right)\right]$
$=\frac{1}{2}\left[\cos \left(45^{\circ}+ A -45^{\circ}+ A \right)\right.$$\left.-\cos \left(45^{\circ}+ A +45^{\circ}- A \right)\right]$
$=\frac{1}{2}\left[\cos 2 A-\cos 90^{\circ}\right]$
$=\frac{1}{2} \cos 2 A$

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