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Prove the trigonometric identity $1+\sin\left(x\right)=\sin\left(x\right)\left(1+\csc\left(x\right)\right)$

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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 RHS (right-hand side)
  • Prove from LHS (left-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 right-hand side (RHS) of the identity

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

$\sin\left(x\right)\left(1+\csc\left(x\right)\right)$

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Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity 1+sin(x)=sin(x)(1+csc(x)). Starting from the right-hand side (RHS) of the identity. Multiply the single term \sin\left(x\right) by each term of the polynomial \left(1+\csc\left(x\right)\right). Simplifying. Since we have reached the expression of our goal, we have proven the identity.

Final answer to the problem

true

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Function Plot

Plotting: $true$

Similar Problems Solved

Prove the identity

$\frac{1}{1-sin\left(x\right)}-\frac{1}{1+\sin\left(x\right)}=2\tan\left(x\right)sec\left(x\right)$

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$\frac{1+\cos2x}{\sin2x}=\cot x$

Prove the identity

$sec\left(x\right)-tan\left(x\right)sin\left(x\right)=\frac{1}{sec\left(x\right)}$

Prove the identity

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

Prove the identity

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

Prove the identity

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

Main Topic: Trigonometric Identities

In mathematics, trigonometric identities are equalities that involve trigonometric functions and are true for every single value of the occurring variables where both sides of the equality are defined.

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