Final Answer
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Factor the polynomial $\sin\left(x\right)^2\cos\left(x\right)^2+\cos\left(x\right)^4$ by it's greatest common factor (GCF): $\cos\left(x\right)^2$
Applying the pythagorean identity: $\sin^2\left(\theta\right)+\cos^2\left(\theta\right)=1$
Any expression multiplied by $1$ is equal to itself
Applying the cosine identity: $\displaystyle\cos\left(\theta\right)=\frac{1}{\sec\left(\theta\right)}$
Since we have reached the expression of our goal, we have proven the identity