Solve the trigonometric equation 1/csc(x)+tan(x)^2=tan(x)^2

 Exercise

$\frac{1}{\csc\left(x\right)}+\tan^2\left(x\right)=\tan^2\left(x\right)$

 

Apply the trigonometric identity: $\frac{1}{\csc\left(\theta \right)}$$=\sin\left(\theta \right)$

$\sin\left(x\right)+\tan\left(x\right)^2=\tan\left(x\right)^2$

 

Grouping all terms to the left side of the equation

$\sin\left(x\right)+\tan\left(x\right)^2-\tan\left(x\right)^2=0$

 

Cancel like terms $\tan\left(x\right)^2$ and $-\tan\left(x\right)^2$

$\sin\left(x\right)=0$

 

The angles where the function $\sin\left(x\right)$ is $0$ are

$x=0^{\circ}+360^{\circ}n,\:x=180^{\circ}+360^{\circ}n$

 

The angles expressed in radians in the same order are equal to

$x=0+2\pi n,\:x=\pi+2\pi n\:,\:\:n\in\Z$

$x=0+2\pi n,\:x=\pi+2\pi n\:,\:\:n\in\Z$

 Try other ways to solve this exercise

Can't find a method? Tell us so we can add it.