Question

If cos 30 = 2cos^215-1 then find cos 15

Answer 1

Answer:

SQRT3 +1/2×SQRT2

Step-by-step explanation:

COS15= COS(45-30)

=COS45COS30+SIN45SIN30

ROOT3 /2ROOT2+1/2ROOT2

Answer 2

$\cos 15=\dfrac{\sqrt{\sqrt{3}+2}}{2}$

Step-by-step explanation:

We have,

$\cos 30=2\cos^215-1$

To find, $\cos 15=?$

∴$\cos 30=2\cos^215-1$

⇒ $2\cos^215-1=\cos 30$

[∵ $\cos 30=\dfrac{\sqrt{3}}{2}$]

⇒ $2\cos^215-1=\dfrac{\sqrt{3}}{2}$

⇒ $2\cos^215=\dfrac{\sqrt{3}}{2}+1$

⇒ $2\cos^215=\dfrac{\sqrt{3}+2}{2}$

⇒ $\cos^215=\dfrac{\sqrt{3}+2}{2\times 2}=\dfrac{\sqrt{3}+2}{4}$

⇒ $\cos 15=\sqrt{\dfrac{\sqrt{3}+2}{4}}$

⇒ $\cos 15=\dfrac{\sqrt{\sqrt{3}+2}}{2}$

∴ $\cos 15=\dfrac{\sqrt{\sqrt{3}+2}}{2}$

Hence, $\cos 15=\dfrac{\sqrt{\sqrt{3}+2}}{2}$