Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity (1-sec(x))/(1+sec(x))=(cos(x)-1)/(cos(x)+1). Starting from the left-hand side (LHS) of the identity. Applying the secant identity: \displaystyle\sec\left(\theta\right)=\frac{1}{\cos\left(\theta\right)}. Combine all terms into a single fraction with \cos\left(x\right) as common denominator. Divide fractions \frac{\frac{\cos\left(x\right)-1}{\cos\left(x\right)}}{1+\sec\left(x\right)} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}.

Prove the trigonometric identity (1-sec(x))/(1+sec(x))=(cos(x)-1)/(cos(x)+1)