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Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$
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$\frac{\sec\left(x\right)-\cos\left(x\right)}{\frac{\sin\left(x\right)}{\cos\left(x\right)}}$
Learn how to solve simplify trigonometric expressions problems step by step online. Simplify the trigonometric expression (sec(x)-cos(x))/tan(x). Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Divide fractions \frac{\sec\left(x\right)-\cos\left(x\right)}{\frac{\sin\left(x\right)}{\cos\left(x\right)}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Multiply the single term \cos\left(x\right) by each term of the polynomial \left(\sec\left(x\right)-\cos\left(x\right)\right). Applying the trigonometric identity: \cos\left(\theta \right)\sec\left(\theta \right) = 1.