What is the general solution for sin(x)=3cos(x),sin(x)cos(x) ?

The general solution for sin(x)=3cos(x),sin(x)cos(x) is No Solution for x\in\mathbb{R}

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sin(x)=3cos(x),sin(x)cos(x)

sin (x) = 3 cos (x), sin (x) cos (x)

No Solution for x \in R

Solution steps

sin (x) = 3 cos (x), sin (x) cos (x)

Rewrite using trig identities

sin (x) = 3 cos (x)

Divide both sides by

cos (x), cos (x) \neq = 0

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

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (x) = 3

tan (x) = 3

Apply trig inverse properties

tan (x) = 3

General solutions for

tan (x) = 3

tan (x) = a \Rightarrow x = arctan (a) + πn

x = arctan (3) + πn

x = arctan (3) + πn

Solutions for the range

sin (x) cos (x)

No Solution for x \in R

tan (x) = \frac{4}{10}

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

3 tan (x^{3}) cot (x) 1 = 0

x, sin (\frac{y}{x}) + cos (\frac{x}{y}) = 0

sin (2 t) cos (t) = 0, 0 \leq t \leq π

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