Final Answer
Step-by-step Solution
Specify the solving method
Starting from the left-hand side (LHS) of the identity
Combine fractions with different denominator using the formula: $\displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}$
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$\frac{1+\tan\left(x\right)}{1-\tan\left(x\right)}+\frac{1+\cot\left(x\right)}{1-\cot\left(x\right)}$
Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (1+tan(x))/(1-tan(x))+(1+cot(x))/(1-cot(x))=0. Starting from the left-hand side (LHS) of the identity. Combine fractions with different denominator using the formula: \displaystyle\frac{a}{b}+\frac{c}{d}=\frac{a\cdot d + b\cdot c}{b\cdot d}. Expand the expression \left(1+\tan\left(x\right)\right)\left(1-\cot\left(x\right)\right)+\left(1+\cot\left(x\right)\right)\left(1-\tan\left(x\right)\right) completely and simplify. Applying the trigonometric identity: \tan\left(\theta \right)\cot\left(\theta \right) = 1.