1
Solved example of trigonometric identities
$\sec\left(x\right)^2+\csc\left(x\right)^2=\frac{1}{\sin\left(x\right)^2\cdot\cos\left(x\right)^2}$
2
Applying the secant identity: $\displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}$
$\frac{1}{\cos\left(x\right)^2}+\csc\left(x\right)^2=\frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2}$
3
Applying the cosecant identity: $\displaystyle\csc\left(\theta\right)=\frac{1}{\sin\left(\theta\right)}$
$\frac{1}{\cos\left(x\right)^2}+\frac{1}{\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2\cos\left(x\right)^2}$
4
Separating the fraction's denominator
$\frac{1}{\cos\left(x\right)^2}+\frac{1}{\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2}\cdot\frac{1}{\cos\left(x\right)^2}$
$\frac{\sin\left(x\right)^2+\cos\left(x\right)^2}{\cos\left(x\right)^2\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2}\cdot\frac{1}{\cos\left(x\right)^2}$
6
Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$
$\frac{1}{\cos\left(x\right)^2\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2}\cdot\frac{1}{\cos\left(x\right)^2}$
7
Separating the fraction's denominator
$\frac{1}{\cos\left(x\right)^2}\cdot\frac{1}{\sin\left(x\right)^2}=\frac{1}{\sin\left(x\right)^2}\cdot\frac{1}{\cos\left(x\right)^2}$
8
Both expressions are equal
true