Question

How do you find the value of `sin75` using the double or half angle formula?

Answer 1

Use the compound angle formula for sin(A+B)

Explanation:

Split the 75 into two angles whose sine and cosine you already know, then use the compound angle formula. Expand and then substitute the known values in, and simplify.

`sin(75)=sin(30+45)`
`sin(30+45)=sin30cos45+sin45cos30`
#sin(75)=1/2*sqrt2/2 +sqrt2/2*sqrt3/2#

`sin(75)=1/4(sqrt2+sqrt6)`