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

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$\frac{\sin\left(x\right)^2-\cos\left(x\right)^2}{\sin\left(x\right)\cos\left(x\right)+\cos\left(x\right)^2}$

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