SOLUTION: Solve the following equations for all x, unless the domain is restricted. sin^2(x) - 5 = cos^2(x) - 1 A. x = 0, 𝛑/2, 𝛑 B. x = 𝛑/2 + 2𝛑n, 𝛑 + 2𝛑n C. x =

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following equations for all x, unless the domain is restricted. sin^2(x) - 5 = cos^2(x) - 1 A. x = 0, 𝛑/2, 𝛑 B. x = 𝛑/2 + 2𝛑n, 𝛑 + 2𝛑n C. x =       Log On


   

Question 1205833: Solve the following equations for all x, unless the domain is restricted.

sin^2(x) - 5 = cos^2(x) - 1
A. x = 0, 𝛑/2, 𝛑
B. x = 𝛑/2 + 2𝛑n, 𝛑 + 2𝛑n
C. x = 0, 𝛑/2, 𝛑, 3𝛑/2
D. no solution
E. x = 0 + 2𝛑n, 𝛑/2 + 2𝛑n
F. x = 𝛑
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

sin%5E2%28x%29+-+5+=+cos%5E2%28x%29+-+1
sin%5E2%28x%29+-+5+=+1-sin%5E2%28x%29+-+1
sin%5E2%28x%29+-+5+=+-sin%5E2%28x%29+
sin%5E2%28x%29+%2Bsin%5E2%28x%29+=5+
2sin%5E2%28x%29+=5+
sin%5E2%28x%29+=5%2F2
sin%28x%29+=sqrt%285%2F2%29
x=sin%5E-1%28sqrt%285%2F2%29%29=> no real roots

answer:
D. no solution

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.


This equation is good to solve it MENTALLY in your head. 


sin^2(x) - 5 = cos^2(x) - 1


Transform it to equivalent equation

    sin^2(x) - cos^2(x) = 4.


But  sin^2(x)  and  cos^2(x)  are non-negative and not greater than 1.


Hence, this equation has no solutions.

Solved (mentally).