The only real solution is theta = 0

For theta < 0 square root of 3 theta is not defined.

For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.

The only real solution is theta = 0

For theta < 0 square root of 3 theta is not defined.

For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.

The only real solution is theta = 0

For theta < 0 square root of 3 theta is not defined.

For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.

The only real solution is theta = 0

For theta < 0 square root of 3 theta is not defined.

For theta > 0, sin theta increases slower than 3*theta and so the sum is always negative.

tan2(theta) + 5*tan(theta) = 0 => tan(theta)*[tan(theta) + 5] = 0=> tan(theta) = 0 or tan(theta) = -5

If tan(theta) = 0 then tan(theta) + cot(theta) is not defined.

If tan(theta) = -5 then tan(theta) + cot(theta) = -5 - 1/5 = -5.2

There are three of them. Granted this means that there are different variations of all three. I'll show you the variations as well. This is coming straight from my Math 1060 (Trigonometry) notebook. Sorry there is no key to represent the angle; Theta.

1. Sin2 (of Theta) + Cos2 (of Theta)= 1

Variations: Sin2 (of Theta) = 1- Cos2 (of Theta)

AND: Cos2 (of Theta) = 1-Sin2 (of Theta)

2. Tan2 (of Theta) + 1 = sec2 (of Theta)

Variations: Tan2 (of Theta) = Sec2 (of Theta) -1

3. 1 + Cot2 (of Theta) = Csc2 (of Theta)

Variations: Cot2 (of Theta) = Csc2 (of Theta) -1