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Prove the trigonometric identity $\sin\left(x\right)\left(\csc\left(x\right)+\sin\left(x\right)\sec\left(x\right)^2\right)=\sec\left(x\right)^2$

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Solving: $\sin\left(x\right)\left(\csc\left(x\right)+\sin\left(x\right)\sec\left(x\right)^2\right)=\sec\left(x\right)^2$
Solve instead: $\sin\left(\csc\left(x\right)+\sin x\sec^2\left(x\right)\right)=\sec^2x$

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

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

$\sin\left(x\right)\left(\csc\left(x\right)+\sin\left(x\right)\sec\left(x\right)^2\right)$

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Learn how to solve proving trigonometric identities problems step by step online. Prove the trigonometric identity sin(x)(csc(x)+sin(x)sec(x)^2)=sec(x)^2. Starting from the left-hand side (LHS) of the identity. Multiply the single term \sin\left(x\right) by each term of the polynomial \left(\csc\left(x\right)+\sin\left(x\right)\sec\left(x\right)^2\right). When multiplying two powers that have the same base (\sin\left(x\right)), you can add the exponents. Since we have reached the expression of our goal, we have proven the identity.

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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