Prove the trigonometric identity $\frac{\cos\left(x\right)^2-\sin\left(x\right)^2}{\cos\left(x\right)^2+\sin\left(x\right)\cos\left(x\right)}=1-\tan\left(x\right)$

Learn how to solve special products problems step by step online. Prove the trigonometric identity (cos(x)^2-sin(x)^2)/(cos(x)^2+sin(x)cos(x))=1-tan(x). Starting from the left-hand side (LHS) of the identity. Factor the polynomial \cos\left(x\right)^2+\sin\left(x\right)\cos\left(x\right) by it's greatest common factor (GCF): \cos\left(x\right). Factor the difference of squares \cos\left(x\right)^2-\sin\left(x\right)^2 as the product of two conjugated binomials. Simplify the fraction \frac{\left(\cos\left(x\right)+\sin\left(x\right)\right)\left(\cos\left(x\right)-\sin\left(x\right)\right)}{\cos\left(x\right)\left(\cos\left(x\right)+\sin\left(x\right)\right)} by \cos\left(x\right)+\sin\left(x\right).