What is the general solution for cot(x)tan(x)=sec(x)csc(x) ?

The general solution for cot(x)tan(x)=sec(x)csc(x) is No Solution for x\in\mathbb{R}

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cot(x)tan(x)=sec(x)csc(x)

cot (x) tan (x) = sec (x) csc (x)

No Solution for x \in R

Solution steps

cot (x) tan (x) = sec (x) csc (x)

Subtract

sec (x) csc (x)

from both sides

cot (x) tan (x) - sec (x) csc (x) = 0

Express with sin, cos

\frac{- 1 + cos ( x ) sin ( x )}{cos ( x ) sin ( x )} = 0

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

- 1 + cos (x) sin (x) = 0

Rewrite using trig identities

- 1 + \frac{sin ( 2 x )}{2} = 0

Move

1

to the right side

\frac{sin ( 2 x )}{2} = 1

Multiply both sides by

2

sin (2 x) = 2

- 1 \leq sin (x) \leq 1

No Solution for x \in R

sin (x + \frac{π}{2}) - sin (x - \frac{π}{2}) = 2

x, tan (x) csc (x) = \frac{1}{f}

sin (x) = \frac{10.7}{71.5}

cos (y) = 1

sec (x) = - 3

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