Question

2) Find the value of cos 15°​

Answer 1

Answer:

0.9659

Step-by-step explanation:

Answer 2

Answer:

$\sf\dfrac{\sqrt{3} + 1}{2\sqrt{2}}$

Step-by-step explanation:

To Find :-

Value of cos15°​

Solution :-

15°​ = 45°​ - 30°​

Applying "cos" on both sides :-

cos15°​ = cos(45°​ - 30°​)

Since, cos(A - B) = cosAcosB + sinAsinB

cos(45°​ - 30°​) = cos45°​cos30°​ + sin45°​sin30°​

cos45°​ = $\sf\dfrac{1}{\sqrt{2}}$

sin45°​ = $\sf\dfrac{1}{\sqrt{2}}$

cos30°​ = $\sf\dfrac{\sqrt{3}}{2}$

sin30°​ = $\sf\dfrac{1}{2}$

$= \dfrac{1}{\sqrt{2}} \times \dfrac{\sqrt{3}}{2} + \dfrac{1}{\sqrt{2}}\times \dfrac{1}{2}$

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

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

cos15°​ = $\sf\dfrac{\sqrt{3} + 1}{2\sqrt{2}}$