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Prove the trigonometric identity $\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

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 Step-by-step Solution 

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Starting from the left-hand side (LHS) of the identity

$\tan\left(x\right)+\cot\left(x\right)$

Learn how to solve equations problems step by step online.

$\tan\left(x\right)+\cot\left(x\right)$

Learn how to solve equations problems step by step online. Prove the trigonometric identity tan(x)+cot(x)=sec(x)csc(x). Starting from the left-hand side (LHS) of the identity. Applying the tangent identity: \displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}. Apply the trigonometric identity: \displaystyle\cot(x)=\frac{\cos(x)}{\sin(x)}. The least common multiple (LCM) of a sum of algebraic fractions consists of the product of the common factors with the greatest exponent, and the uncommon factors.

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Prove from RHS (right-hand side)Express everything into Sine and Cosine

Main Topic: Equations

In mathematics, an equation is a statement of an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions.