Yes. Both expressions are the same.
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Let x = theta, since it's easier to type, and is essentially the same variable. Since tan^2(x)=tan(x), you know that tan(x) must either be 1 or zero for this statement to be true. So let tan(x)=0, and solve on your calculator by taking the inverse. Similarly for, tan(x)=1
Tan^2
Sin squared is equal to 1 - cos squared.
sin is short for sine. Sin(x) means the ratio of the side of a right triange opposite the angle 'x' divided by the length of the hypotenuse. cos is short for cosine. Cos(x) is equal to the similar ratio of the side adjacent to the angle 'x' divided by the length of the hypotenuse. tan is short for tangent. Tan(x) is equal to the ratio of the opposite side divided by the adjacent side. This is the same as sin(x)/cos(x).
There is not much that can be done by way of simplification. Suppose arccot(y) = tan(x) then y = cot[tan(x)] = 1/tan(tan(x)) Now cot is NOT the inverse of tan, but its reciprocal. So the expression in the first of above equation cannot be simplified further. Similarly tan[tan(x)] is NOT tan(x)*tan(x) = tan2(x)