Question

Find the value of :-
Cos75 - cos15

Answer 1

Answer:

$\frac{\sqrt{6} }{2}$

Explanation:

Given :

To find the value of :

Cos 75° - Cos 15°

Solution :

We know that,

$Cos A - Cos B = 2 Cos (\frac{A+B}{2})Cos(\frac{A - B}{2} )$

⇒ A + B = 75° + 15° = 90°

⇒ $\frac{A+B}{2} = \frac{90}{2}$ = 45°

⇒ A - B = 75° - 15° = 60°

⇒ $\frac{A-B}{2} = \frac{60}{2}$ = 30°

⇒ Cos 75° - Cos 15° = 2 Cos 45° Cos 30° = $2(\frac{1}{\sqrt{2}})(\frac{\sqrt{3}}{2}) = \frac{\sqrt{3} }{\sqrt{2}}$

By Multiplying & Dividing by $\sqrt{2}$,

⇒ $\frac{\sqrt{3} }{\sqrt{2} } \times \frac{\sqrt{2} }{\sqrt{2} } = \frac{\sqrt{6} }{2}$