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Prove the trigonometric identity $\cot\left(x-\frac{\pi }{2}\right)=-\tan\left(x\right)$

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Solution

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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

Learn how to solve proving trigonometric identities problems step by step online.

$\cot\left(x-\frac{\pi }{2}\right)$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity cot(x-pi/2)=-tan(x). Starting from the left-hand side (LHS) of the identity. Apply sum-angle identity for cotangent function: \displaystyle\cot\left(a\pm b\right)=\frac{\cot a\cot b\mp 1}{\cot b \pm \cot a}. Multiply -1 times -1. Calculating the cotangent of \frac{\pi }{2} degrees.

Final answer to the problem

true

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Similar Problems Solved

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$\tan\left(x\right)+\cot\left(x\right)=\sec\left(x\right)\csc\left(x\right)$

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Prove the identity

$\sec x-\sin x\tan x=\cos x$

Main Topic: Proving Trigonometric Identities

To prove a trigonometric identity, you have to show that one side of the equation can be transformed into the other side.

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