Question

The value of $\cos {48}^0.\cos {12}^0$ is

• A. $\frac{1-\sqrt{5}}{8}$
• B. $\frac{\sqrt{5}+3}{8}$
• C. $\frac{\sqrt{5}-1}{8}$
• D. $\frac{\sqrt{5}+1}{8}$

Answer 1

Answer: (B)

$\frac{\sqrt{5}+3}{8}$

Formula:

$2\cos A\cos B=\cos (A+B)+\cos (A-B)$

$\cos {48}^0.\cos {12}^0=\frac{1}{2}[\cos {60}^0+\cos {36}^0]$
$=\frac{1}{2}[\frac{1}{2}+\frac{\sqrt{5}+1}{4}]$
$=\frac{\sqrt{5}+3}{8}$
Because $\cos {36}^0=\frac{\sqrt{5}+1}{4}$
Hence, option 'B' is correct.