Question

State true or false.

$\cos {48}^o\cos {12}^o=\frac{3+\sqrt{5}}{8}$

• A. True
• B. False

Answer 1

The correct option is A True

$LHS=\cos {48}^{\circ }\cos {12}^{\circ }$

$=\frac{\cos ({48}^{\circ }+{12}^{\circ })+\cos ({48}^{\circ }-{12}^{\circ })}{2}$

$=\frac{\cos {60}^{\circ }+\cos {36}^{\circ }}{2}$

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

$=\frac{2}{8}+\frac{\sqrt{5}+1}{8}$

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

So the relation is true