What is the general solution for sin(x)tan(x)= 1/(cot(x)) ?

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

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sin(x)tan(x)= 1/(cot(x))

sin (x) tan (x) = \frac{1}{cot ( x )}

No Solution for x \in R

Solution steps

sin (x) tan (x) = \frac{1}{cot ( x )}

Subtract

\frac{1}{cot ( x )}

from both sides

sin (x) tan (x) - \frac{1}{cot ( x )} = 0

Simplify

sin (x) tan (x) - \frac{1}{cot ( x )} : \frac{sin ( x ) tan ( x ) cot ( x ) - 1}{cot ( x )}

\frac{sin ( x ) tan ( x ) cot ( x ) - 1}{cot ( x )} = 0

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

sin (x) tan (x) cot (x) - 1 = 0

Rewrite using trig identities

- 1 + sin (x) = 0

Move

1

to the right side

sin (x) = 1

General solutions for

sin (x) = 1

x = \frac{π}{2} + 2 πn

Since the equation is undefined for:

\frac{π}{2} + 2 πn

No Solution for x \in R

0 = - 2 sin (x) - 1

x, z = sin (2 x + 3 y)

2 sin (3 θ) = 2

2 tan (x) csc (x) + 2 csc (x) + tan (x) = - 1

4 cos (x) + 1 = 2 cos (x)

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