Question

Without using calculator, find sin (15⁰).​

Answer 1

Answer:

The actual value of sin 15 degrees is (√3−1)/(2√2).

Answer 2

Answer:

The value of sin (15⁰) = ($\sqrt{3}$ - 1  )/ 2$\sqrt{2}$      

Step-by-step explanation:

Given : to find Sin(15°) without using calculator

Solution : We can write Sin15 = Sin (60-45)

               Identity Sin (a-b) = Sin(a)Cos(b) - Cos(a)Sin(b)

                             Sin (60-45) = Sin60 x Cos45 - Cos60 x Sin45

            We know, Sin60 = $\sqrt{3}$/2, Sin45 = Cos45 = 1/$\sqrt{2}$, Cos60 = 1/2

             ∴ Sin(60-45) = $\sqrt{3}$/2 x 1/$\sqrt{2}$ - 1/2 x 1/$\sqrt{2}$

                                  = $\sqrt{3}$/2$\sqrt{2}$ - 1/2$\sqrt{2}$

                                  = ($\sqrt{3}$ - 1  )/2$\sqrt{2}$