Final Answer
Step-by-step Solution
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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): $\cos\left(x\right)$
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$\frac{\cos\left(x\right)^2-\sin\left(x\right)^2}{\cos\left(x\right)^2+\sin\left(x\right)\cos\left(x\right)}$
Learn how to solve trigonometric identities 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).