Question

Q. 2
1) Find the value of cos 15°​

Answer 1

Answer:

ANSWER IS COS 15 = √3+1/2√2

Answer 2

Step-by-step explanation:

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

Step-by-step explanation:

We have,

➪$\cos 30=2\cos^2 15-1cos30=2cos$

➪$\rm To \:find, \:the \:value \:of \:\cos 15cos15 = ?$

$\cos 30=2\cos^2 15-1cos30=2cos$

$⇒ 2\cos^2 15=\cos 30+12cos$

$⇒ 2\cos^2 15=\dfrac{\sqrt{3}}{2}+12cos$

We know that,

$✵\cos 30=\dfrac{\sqrt{3}}{2}$✵

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

$⇒ \cos^2 15=\dfrac{\sqrt{3}+2}{4}$

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

$⇒ \cos 15=\dfrac{\sqrt{\sqrt{3}+2}}{2}cos15$

✵$⇒ \cos 15=\dfrac{{\sqrt{3}+1}}{2\sqrt{2}}cos15$✵

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

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