Verified Answer :
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 : 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, \(\frac{\sqrt{3}+1}{2\sqrt{2}}\)