serafimharmane1782 serafimharmane1782
  • 07-09-2020
  • Mathematics
contestada

How do you solve the equation 2cos^2 - cosx = 0 for all solutions?

Respuesta :

abidemiokin
abidemiokin abidemiokin
  • 08-09-2020

Answer:

π/2 and π/3

Step-by-step explanation:

Given the equation 2cos²x - cosx = 0, to find the solution to the equation, we will follow the following step.

let P = cosx

The equation becomes 2P²-P = 0

P(2P-1) = 0

P = 0 and 2P-1 = 0

P= 0 and P = 1/2

Since P = cosx

cosx = 0 and cos(x) =  1/2

If cos(x) = 0

x = cos⁻¹0

x = 90⁰

x = π/2

If cos(x) = 1/2

x = cos⁻¹1/2

x = 60⁰

x = π/3

Hence the solutions to the equation are π/2 and π/3.

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