Step-by-step explanation:
cos(3x) − 3 cos x = cos(2x) + 1
Use triple and double angle formulas.
(4 cos³x − 3 cos x) − 3 cos x = (2 cos²x − 1) + 1
Simplify.
4 cos³x − 6 cos x = 2 cos²x
4 cos³x − 2 cos²x − 6 cos x = 0
2 cos³x − cos²x − 3 cos x = 0
Factor.
cos x (2 cos²x − cos x − 3) = 0
cos x (cos x + 1) (2 cos x − 3) = 0
Solve.
cos x = 0 → x = 90°, 270°
cos x + 1 = 0 → x = 180°
2 cos x − 3 = 0 → no solution
Answer:
1 solution
Step-by-step explanation:
The solution is the intersection point, which is at (3, -2)
Answer:
B
Step-by-step explanation:
Natural Numbers Are Positive Whole Numbers, So Not A.
Whole Numbers Are Numbers With No Decimal, So Not B.
Integers Are Numbers, So C.
Rational Numbers Can Be Written As A Fraction, So D.
Irrational Numbers Cannot Be Written As A Fraction, So Not E.
Real Numbers Are Rational Numbers, So F.