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

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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
  • Load more...
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1

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

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

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

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity sin(x-pi/2)=-cos(x). Starting from the left-hand side (LHS) of the identity. Using the sine of a sum formula: \sin(\alpha\pm\beta)=\sin(\alpha)\cos(\beta)\pm\cos(\alpha)\sin(\beta), where angle \alpha equals x, and angle \beta equals -\frac{\pi }{2}. The sine of \frac{\pi }{2} equals 1. Multiply -1 times 1.

Final answer to the problem

true

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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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