Prove the trigonometric identity $\frac{1+\cos\left(2x\right)}{\sin\left(2x\right)}=\cot\left(x\right)$

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Final answer to the problem

true

Step-by-step Solution

How should I solve this problem?

  • Prove from LHS (left-hand side)
  • Prove from RHS (right-hand side)
  • Express everything into Sine and Cosine
  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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Starting from the left-hand side (LHS) of the identity

$\frac{1+\cos\left(2x\right)}{\sin\left(2x\right)}$

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$\frac{1+\cos\left(2x\right)}{\sin\left(2x\right)}$

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Learn how to solve definite integrals problems step by step online. Prove the trigonometric identity (1+cos(2x))/sin(2x)=cot(x). Starting from the left-hand side (LHS) of the identity. Simplify 1+\cos\left(2x\right) into 2\cos\left(x\right)^2 by applying trigonometric identities. Using the sine double-angle identity: \sin\left(2\theta\right)=2\sin\left(\theta\right)\cos\left(\theta\right). Simplify the fraction \frac{2\cos\left(x\right)^2}{2\sin\left(x\right)\cos\left(x\right)} by 2.

Final answer to the problem

true

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Function Plot

Plotting: $true$

Main Topic: Definite Integrals

Given a function f(x) and the interval [a,b], the definite integral is equal to the area that is bounded by the graph of f(x), the x-axis and the vertical lines x=a and x=b

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