Solve the trigonometric equation6cos(2𝑡)−2=4to find an exact solution on the interval [0,𝜋]

Sure, let's solve the trigonometric equation step by step.

1. First, we need to isolate the cosine function. We can do this by adding 2 to both sides of the equation and then dividing by 6. This gives us:

   cos(2t) = (4+2)/6 = 1

2. Now we need to solve for 2t. The cosine of what angle gives us 1? Well, cos(0) = 1 and cos(2π) = 1. But we need to consider that 2t is inside the cosine function, so we need to find the solutions in the interval [0, 2π] to cover all possible values for t in the interval [0, π]. So, 2t = 0 and 2t = 2π are the solutions.

3. Finally, we solve for t by dividing each solution by 2:

   t = 0/2 = 0 t = 2π/2 = π

So, the solutions to the equation 6cos(2t) - 2 = 4 on the interval [0, π] are t = 0 and t = π.