Question

Find an exact value. cos 15°

Answer 1

Your awnser is going to be in a fraction form. Im on my laptop so there is no symbol for square root but your answer is going to be 
 The square root of 6+ the square root of 2 (Thats the top half of the fraction) over 4 (bottom half of the fraction)

Answer 2

Answer : The exact value of $\cos 15^o$ is, $\frac{\sqrt{3}+1}{2\sqrt{2}}$

Step-by-step explanation :

As we are given that: $\cos 15^o$

Now we have to calculate the exact value of $\cos 15^o$.

We can write $\cos 15^o$ as,

$\cos 15^o=\cos (45^o-30^o)$

Using identity :

$\cos (A-B)=(\cos A\times \cos B)+(\sin A\times \sin B)$

$\cos (45^o-30^o)=(\cos 45^o\times \cos 30^o)+(\sin 45^o\times \sin 30^o)$

As, we know that:

$\sin 45^o=\frac{1}{\sqrt{2}}\\\\\cos 45^o=\frac{1}{\sqrt{2}}\\\\\sin 30^o=\frac{1}{2}\\\\\cos 30^o=\frac{\sqrt{3}}{2}$

Now put all the given values in the above expression, we get:

$\cos (45^o-30^o)=(\frac{1}{\sqrt{2}}\times \frac{\sqrt{3}}{2})+(\frac{1}{\sqrt{2}}\times \frac{1}{2})$

$\cos (45^o-30^o)=(\frac{\sqrt{3}}{2\sqrt{2}})+(\frac{1}{2\sqrt{2}})$

$\cos (45^o-30^o)=\frac{\sqrt{3}+1}{2\sqrt{2}}$

So,

$\cos 15^o=\frac{\sqrt{3}+1}{2\sqrt{2}}$

Thus, the exact value of $\cos 15^o$ is, $\frac{\sqrt{3}+1}{2\sqrt{2}}$