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# Prove the trigonometric identity $\sec\left(x\right)=\frac{\sin\left(2x\right)}{\sin\left(x\right)}-\frac{\cos\left(2x\right)}{\cos\left(x\right)}$

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true

##  Step-by-step Solution 

Problem to solve:

$\sec\left(x\right)=\frac{\sin\left(2x\right)}{\sin\left(x\right)}-\frac{\cos\left(2x\right)}{\cos\left(x\right)}$

Specify the solving method

1

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

$\sec\left(x\right)$
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Since the expression on the left of the equality is too simple, it's not clear how we can proceed to prove the identity from there. Although we know that the identity is true

true

true

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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

### Main topic:

Trigonometric Integrals

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