Question: how to find the value of sin(15)?

Question: how to find the value of sin(15)?

Solution :

We shall write 15⁰=45⁰-30⁰

And apply Sin(A-B)  formula

Sin(A-B) =Sin(A)Cos(B)-Cos(A)Sin(A)

Therefore

Sin(15⁰) = Sin(45⁰-30⁰) =Sin(45⁰)Cos(30⁰)-Cos(45⁰)Sin(30⁰)

 Now we shall substitute following values into above formulas

Sin(45⁰) =1/√2 , Cos(30⁰) = √3/2 , Cos(45⁰) = 1/√2 , Sin(30⁰) =1/2

That is

 Sin(15⁰  )=(1/√2)( √3/2)-(1/√2)( ½)=1/(2√2) (√3-1)