Write out one of the sum and difference identities Describe

Write out one of the sum and difference identities. Describe how you can use this identity to find trig values for an angle measuring 15 degrees. --This is for a discussion topic my teacher does not want to see equations she wants it explained as if you were telling somebody the steps.

Solution

Let me first write one of the sum identity

Sin(A+B)= Sin A Cos B+ Cos A Sin B

And difference identity is

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

Lets check out the value of sin 15 using difference identity.

15=45-30

So we can write Sin 15 as

Sin (45-30)

Now we use the difference identity

Sin(45-30)=Sin 45 Cos 30 - Cos 45 Sin 30

Sin(45-30) = 1/sqrt2 * sqrt3/2 - 1/sqrt2 *1/2

Sin(45-30) = (sqrt3-1)/2sqrt2

Multiplying both top and bottom by sqrt 2,

         Sin (45-30) = sqrt 2 (sqrt3-1)/2sqrt 2*sqrt 2

              Sin (45-30)= sqrt2 (sqrt3 -1)/4

Therefore Sin 15= sqrt2(sqrt3 -1)/4

In this way by using sum and difference identity,we can find out the values without using calculator