Question

Using the formula, $cosA=\sqrt{\frac{1+cos2A}{2}},$ find the value of $cos{30}^0$, it being given that $cos{60}^0=\frac{1}{2}.$

Answer 1

We have,

$\cos {60}^0=\frac{1}{2}$

We know that

$\cos A=\sqrt{\frac{1+\cos 2A}{2}}$

Put $A={30}^0$,

$\cos {30}^0=\sqrt{\frac{1+\cos 2\times {30}^0}{2}}$

$\cos {30}^0=\sqrt{\frac{1+\cos {60}^0}{2}}$

$\cos {30}^0=\sqrt{\frac{1+\frac{1}{2}}{2}}$

$\cos {30}^0=\sqrt{\frac{3}{4}}$

$\cos {30}^0=\frac{\sqrt{3}}{2}$

Hence, this is the answer.