Question

Use trigonometric identities and algebraic methods, as necessary, to solve the following trigonometric equation. Please identify all possible solutions by including allanswers in [0, 2n) and indicating the remaining answers by using n to represent any integer, Round your answer to four decimal places, if necessary. If there is nosolution, indicate "No Solution."cos? (x) + 9cos(x) = 5cos(x) + 5

Answer 1

Given the equation:

cos²(x) + 9cos(x) = 5cos(x) + 5

cos²(x) + 9cos(x) - 5 cos(x) - 5 = 0

cos²(x) + 4cos(x) - 5 = 0

[cos(x) + 5][cos(x) - 1] = 0

cos (x) = - 5 x ∉ ℝ; so:

cos (x) = 1

Then;

x = 0, and x = 2π