What is the general solution for csc(A)*tan(A)=sin(A) ?

The general solution for csc(A)*tan(A)=sin(A) is No Solution for A\in\mathbb{R}

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csc(A)*tan(A)=sin(A)

csc (A) \cdot tan (A) = sin (A)

No Solution for A \in R

Solution steps

csc (A) tan (A) = sin (A)

Subtract

sin (A)

from both sides

csc (A) tan (A) - sin (A) = 0

Express with sin, cos

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

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

1 - cos (A) sin (A) = 0

Rewrite using trig identities

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

Move

1

to the right side

- \frac{sin ( 2 A )}{2} = - 1

Multiply both sides by

2

- sin (2 A) = - 2

Divide both sides by

- 1

sin (2 A) = 2

- 1 \leq sin (x) \leq 1

No Solution for A \in R

cos (x) = \frac{2}{3}

(sec (3 x) - 2) (tan (2 x) - 1) = 0

cos (2 x) \cdot 2 - 2 cos (x) = 0

- 2 sin (2 x) = \frac{π}{12}

cos (x) = \frac{sec ( x )}{4}

What is the general solution for csc(A)*tan(A)=sin(A) ?
The general solution for csc(A)*tan(A)=sin(A) is No Solution for A\in\mathbb{R}