Question

Prove that cos 48° . cos 12° = $\frac{3 + \sqrt{5}}{8}$.

Answer 1

Answer:

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

Step-by-step explanation:

Formula used:

cosA cosB = 1/2[cos(A+B)+cos(A-B)]

cos 48° . cos 12°

$=\frac{1}{2}[2cos48\:cos12]$

$=\frac{1}{2}[cos(48+12)+cos(48-12)]$

$=\frac{1}{2}[cos60+cos36]$

$=\frac{1}{2}[\frac{1}{2}+\frac{ \sqrt{5}+1}{4}]$

$=\frac{1}{2}[\frac{ \sqrt{5}+3}{4}]$

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