Question

cosx(cosx-2)=1

Answer 1

Use distributive property.

Answer 2

Sorry what? I'm doing lower sixth maths in England I don't know what that means?

Answer 3

a(b+c)=ab+ac

Answer 4

England?

Answer 5

I know how to expand it, I don't know how to solve it...

Answer 6

First expand. Then you get a quadratic equation in cos x. Put t=cos x and solve for t.

Answer 7

@meshlogic It's okay since you are new :)

Answer 8

When I expand I end up with cos^2x - 2 cosx -1 = 0 How do I solve that it makes no sence

Answer 9

Put t= cos x. You get a quadratic equation in t. Solve for t.

Answer 10

I would then have t^2 - 2t -1 = 0 which cannot be factorised. (t - 1)(t + 1) doesn't expand to what I have...

Answer 11

Complete the square

Answer 12

I'll try

Answer 13

I now have -cosx = + or - 1

Answer 14

Completing the square, did you get:

\[t^2-2+1 -1=0+1\\t^2-2+1=2\\(t-1)(t-1)=2\]
?

Answer 15

oh I see where I went wrong, thank you :-)

Answer 16

Good work @meshlogic :)

Answer 17

put the values for cos into a cast diagram and got the correct answer, thanks guys :-)