Analysis help (2 Viewers)

[lorderok]

I'm in accelerated analysis and I need help solving this equation. I'm only in 10th grade, so i need the explanation for it. Equation: 2cos²(x)-cos(x)=2-sec(x)
Please help!I'm also american, if it helps, so, You may want to check what time it is in detroit.

 

[bored of sc]

I'm in accelerated analysis and I need help solving this equation. I'm only in 10th grade, so i need the explanation for it. Equation: 2cos²(x)-cos(x)=2-sec(x)
Please help!I'm also american, if it helps, so, You may want to check what time it is in detroit.

2cos²x -cosx = 2-secx

2cos²x -cosx = 2-(1/cosx) ---- write sec in terms of cos i.e. secx = 1/cosx
2cos³x -cos²x -2cosx +1 = 0 ---- mutliply through by cosx to destroy the fraction and move all terms to the left hand side of the equation
cos²x(2cosx-1) -1(2cosx-1) = 0 ---- group in pairs to factorise
(cos²x-1)(2cosx-1) = 0 ---- rewrite factorisation
(cosx-1)(cosx+1)(2cosx-1) = 0 ---- recognise difference of two squares and factorise accordingly

cosx -1 = 0, cosx +1 = 0, 2cosx -1 = 0 ---- let each factor equal zero to solve for x

cosx -1 = 0
cosx = 1
x = 0, 360, 720 etc

cosx +1 = 0
cosx = -1
x = 180, 540 etc

2cosx -1 = 0
2cosx = 1
cosx = 1/2
x = 60, 300, 420 etc

You should use general solutions to find all values for x. I can't remember the formulae for general solutions so I'll leave it up to you.

 

[Aplus]

Accelerated analysis...
American education always confuses the hell out of me.