Question

if cos 30 is equal to 2 cos square 15 - 1 then the value of cos 15 is equal to​

Answer 1

Step-by-step explanation:

cos (30) = 2 x cos²(15)

cos²(15) = cos (30) / 2

cos (15) √[ cos (30) / 2]

Answer 2

$\cos 15=\dfrac{{\sqrt{3}+1}}{2\sqrt{2}}$

Step-by-step explanation:

We have,

$\cos 30=2\cos^2 15-1$

To find, the value of $\cos 15 = ?$

$\cos 30=2\cos^2 15-1$

⇒ $2\cos^2 15=\cos 30+1$

⇒ $2\cos^2 15=\dfrac{\sqrt{3}}{2}+1$

We know that,

$\cos 30=\dfrac{\sqrt{3}}{2}$

⇒ $2\cos^2 15=\dfrac{\sqrt{3}+2}{2}$

⇒ $\cos^2 15=\dfrac{\sqrt{3}+2}{4}$

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

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

⇒ $\cos 15=\dfrac{{\sqrt{3}+1}}{2\sqrt{2}}$

∴ The value of $\cos 15=\dfrac{{\sqrt{3}+1}}{2\sqrt{2}}$

Thus, the value of $\cos 15$ is equal to $\dfrac{{\sqrt{3}+1}}{2\sqrt{2}}.$