find the fundamental solution set (FSS) for(cos2θ)(tanθ+1)=0

To find the fundamental solution set (FSS) for the equation (cos2θ)(tanθ + 1) = 0, we need to solve it for values of θ that satisfy the equation.

First, let's consider the equation (cos2θ)(tanθ + 1) = 0. To understand when this equation is equal to zero, we need to set each individual factor equal to zero and solve.

1. cos2θ = 0:
We know that cos2θ = 0 when θ = (2n + 1)(π/2), where n is an integer.

2. tanθ + 1 = 0:
Subtracting 1 from both sides, we have:
tanθ = -1

The tangent function is equal to -1 when θ = (2n + 1)(π/4), where n is an integer.

Now, we combine the solutions obtained from both equations to find the FSS for (cos2θ)(tanθ + 1) = 0.

The FSS is the set of values for θ that satisfy the equation. In this case, the FSS is:
θ = (2n + 1)(π/2) for n being an integer
θ = (2n + 1)(π/4) for n being an integer

Therefore, the fundamental solution set for (cos2θ)(tanθ + 1) = 0 is:
θ = (2n + 1)(π/2), (2n + 1)(π/4) for n being an integer.