What is the general solution for (cot(x)+1/(cot(x)))/(cos(x))=sec(x) ?

The general solution for (cot(x)+1/(cot(x)))/(cos(x))=sec(x) is No Solution for x\in\mathbb{R}

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(cot(x)+1/(cot(x)))/(cos(x))=sec(x)

\frac{cot ( x ) + \frac{1}{c o t ( x )}}{cos ( x )} = sec (x)

No Solution for x \in R

Solution steps

\frac{cot ( x ) + \frac{1}{c o t ( x )}}{cos ( x )} = sec (x)

Subtract

sec (x)

from both sides

\frac{cot ^{2} ( x ) + 1}{cot ( x ) cos ( x )} - sec (x) = 0

Simplify

\frac{cot ^{2} ( x ) + 1}{cot ( x ) cos ( x )} - sec (x) : \frac{cot ^{2} ( x ) + 1 - sec ( x ) cot ( x ) cos ( x )}{cot ( x ) cos ( x )}

\frac{cot ^{2} ( x ) + 1 - sec ( x ) cot ( x ) cos ( x )}{cot ( x ) cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

cot^{2} (x) + 1 - sec (x) cot (x) cos (x) = 0

Rewrite using trig identities

1 - cot (x) + cot^{2} (x) = 0

Solve by substitution

cot (x) = \frac{1}{2} + i \frac{3}{2}, cot (x) = \frac{1}{2} - i \frac{3}{2}

cot (x) = \frac{1}{2} + i \frac{3}{2} :

No Solution

cot (x) = \frac{1}{2} - i \frac{3}{2} :

No Solution

Combine all the solutions

No Solution for x \in R

sec (θ) = 2, (tan (θ) - sin (θ))^{2} + (1 - cos (θ))^{2}

(1 + csc (A)) (1 - csc (A)) = - cot (A)

6 cos^{2} (3 x) - cos (3 x) - 2 = 0

cos (2 x) - 3 cos (x) + 1 = 0

2 cos^{2} (x) - cos (x) - 1 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

What is the general solution for (cot(x)+1/(cot(x)))/(cos(x))=sec(x) ?
The general solution for (cot(x)+1/(cot(x)))/(cos(x))=sec(x) is No Solution for x\in\mathbb{R}