How do you solve cos 2x= cos x-1?

1 Answer
Jim G.
Jan 29, 2016

x = 60^@ , 90^@ , 270^@ and 300^@

Explanation:

Using trig formulae:

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

Replace cos2x by (2cos^2 x - 1 )

cos2x = cox - 1 becomes 2cos^2x - 1 = cosx - 1

This is a quadratic function and to solve equate to zero.

hence : 2cos^2x - 1 - cosx + 1 = 0

simplifies to : 2cos^2x - cosx = 0

factorise : cosx (2cosx - 1 ) = 0

→ cosx = 0 → x = 90^@ , 270^@

and cosx = 1/2 →x = 60^@ , 300^@

These solutions are in the interval 0 < x ≤ 360

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