How do you prove that sin30=3sinx-4sin²x?

1 Answer
Mar 15, 2018

x=(-1)^k*arcsin(1/4)+180k, k in ZZ and
x=(-1)^k*30^@+180k, k in ZZ

Explanation:

Use substitution to solve this equation. Substitute sinx with t.

3t-4t^2=sin30^@ and sin30^@=1/2 therefore,
3t-4t^2-1/2=0

Solve the quadratic equation and get two possible answers.

x=(-1)^k*arcsin(1/4)+180k, k in ZZ and
x=(-1)^k*30^@+180k, k in ZZ