# Answer to Question #10219 in Calculus for m Khan

Question #10219

Find all the solutions in the interval [0,2π) for the equation cos² x - 2cosx - 3 = 0

Show your Work.

Show your Work.

Expert's answer

Find all the solutions in the interval [0,2π) for the equation cos² x - 2cosx - 3 = 0.

cos² x - 2cosx - 3 = 0 ==>

(cos x + 1)(cos x - 3) = 0 ==>

cos x = -1& ==> x = π (= 180°);

cos x = 3 - impossible value.

The only value for x in the interval [0,2π) is π.

cos² x - 2cosx - 3 = 0 ==>

(cos x + 1)(cos x - 3) = 0 ==>

cos x = -1& ==> x = π (= 180°);

cos x = 3 - impossible value.

The only value for x in the interval [0,2π) is π.

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