Prove the trigonometric identity $\cos\left(x\right)=\sec\left(x\right)-\sin\left(x\right)\tan\left(x\right)$

Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity cos(x)=sec(x)-sin(x)tan(x). Starting from the right-hand side (RHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Multiplying the fraction by \sin\left(x\right). Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}.