What is the general solution for tan(x)+cot(x)=3,=tan(3x)+cot(3x) ?

The general solution for tan(x)+cot(x)=3,=tan(3x)+cot(3x) is No Solution for x\in\mathbb{R}

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tan(x)+cot(x)=3,=tan(3x)+cot(3x)

tan (x) + cot (x) = 3, = tan (3 x) + cot (3 x)

No Solution for x \in R

Solution steps

tan (x) + cot (x) = 3, = tan (3 x) + cot (3 x)

Subtract

3

from both sides

tan (x) + cot (x) - 3 = 0

Rewrite using trig identities

- 3 + cot (x) + \frac{1}{cot ( x )} = 0

Solve by substitution

cot (x) = \frac{3 + 5}{2}, cot (x) = \frac{3 - 5}{2}

cot (x) = \frac{3 + 5}{2}, = tan (3 x) + cot (3 x) :

No Solution

cot (x) = \frac{3 - 5}{2}, = tan (3 x) + cot (3 x) :

No Solution

Combine all the solutions

No Solution for x \in R

x, cos^{2} (x) = sin^{2} (x)

3 cot (x) - 1 = cot^{2} (x)

sin (x) = - 0.974

sin (x) = - 0.978

cos (t) = \frac{15}{17}

What is the general solution for tan(x)+cot(x)=3,=tan(3x)+cot(3x) ?
The general solution for tan(x)+cot(x)=3,=tan(3x)+cot(3x) is No Solution for x\in\mathbb{R}