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

1 Answer
KPaukstis
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#

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