SOLUTION: Solve the following equations for all x, unless the domain is restricted. sin(x) = 2 cos^2(x) - 1 A. 𝛑/6 + 2𝛑n, 5𝛑/6 + 2𝛑n, 7𝛑/6 + 2𝛑n, 11𝛑/6 + 2𝛑n

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following equations for all x, unless the domain is restricted. sin(x) = 2 cos^2(x) - 1 A. 𝛑/6 + 2𝛑n, 5𝛑/6 + 2𝛑n, 7𝛑/6 + 2𝛑n, 11𝛑/6 + 2𝛑n       Log On


   

Question 1205837: Solve the following equations for all x, unless the domain is restricted.
sin(x) = 2 cos^2(x) - 1
A. 𝛑/6 + 2𝛑n, 5𝛑/6 + 2𝛑n, 7𝛑/6 + 2𝛑n, 11𝛑/6 + 2𝛑n
B. 𝛑/6 + 2𝛑n, 5𝛑/6 + 2𝛑n
C. 𝛑/6 + 2𝛑n, 11𝛑/6 + 2𝛑n
D. 𝛑/6 + 2𝛑n, 5𝛑/6 + 2𝛑n, 3𝛑/2 + 2𝛑n
E. 5𝛑/6 + 2𝛑n
F. 3𝛑/2 + 2𝛑n
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sin%28x%29+=+2+cos%5E2%28x%29+-+1
use identity cos%5E2%28x%29+=+1-sin%5E2%28x%29

sin%28x%29+=+2+%281-sin%5E2%28x%29%29+-+1
sin%28x%29+=+2+-2sin%5E2%28x%29+-+1
sin%28x%29+=+1+-2sin%5E2%28x%29+
2sin%5E2%28x%29+%2Bsin%28x%29+-1=0.....factor
2sin%5E2%28x%29+-sin%28x%29%2B2sin%28x%29+-1=0
%282sin%5E2%28x%29+-sin%28x%29%29%2B%282sin%28x%29+-1%29=0
sin%28x%29%282sin%28x%29+-1%29%2B%282sin%28x%29+-1%29=0
%28sin%28x%29+%2B+1%29+%282sin%28x%29+-+1%29=0

solutions:
%28sin%28x%29+%2B+1%29+=0 =>sin%28x%29+=-+1 => x=sin%5E-1%28-1%29
%282sin%28x%29+-+1%29=0=>2sin%28x%29+=+1 =>sin%28x%29+=+1%2F2 => x=sin%5E-1%281%2F2%29
x=sin%5E-1%28-1%29=-pi%2F2
general solution: x=2pi-pi%2F2%2B2pi%2An=3pi%2F2%2B2pi%2An
x=sin%5E-1%281%2F2%29=pi%2F6
general solution:
x=pi%2F6%2B2pi%2An
x=5pi%2F6%2B2pi%2An

combine all solutions
x=3pi%2F2%2B2pi%2An
x=pi%2F6%2B2pi%2An
x=5pi%2F6%2B2pi%2An
answer is:
D. 𝛑/6 + 2𝛑n, 5𝛑/6 + 2𝛑n, 3𝛑/2 + 2𝛑n