Simplify the trigonometric expression tan(x)^2-cot(x)^2csc(x)^2

 Exercise

$\tan^2\left(x\right)-\cot^2\left(x\right)+\csc^2\left(x\right)$

 

Applying the trigonometric identity: $\cot\left(\theta \right)^2 = \csc\left(\theta \right)^2-1$

$\tan\left(x\right)^2-\left(\csc\left(x\right)^2-1\right)+\csc\left(x\right)^2$

 

Solve the product $-\left(\csc\left(x\right)^2-1\right)$

$\tan\left(x\right)^2-\csc\left(x\right)^2+1+\csc\left(x\right)^2$

 

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

$\tan\left(x\right)^2+1$

 

Applying the trigonometric identity: $1+\tan\left(\theta \right)^2 = \sec\left(\theta \right)^2$

$\sec\left(x\right)^2$

 Why is tan(x)^2+1 = sec(x)^2 ?

$\sec\left(x\right)^2$

 Try other ways to solve this exercise

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