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Prove the trigonometric identity $\left(1+\sin\left(x\right)\right)\left(1-\sin\left(x\right)\right)=\cos\left(x\right)^2$

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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 trigonometric identities problems step by step online.

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

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Learn how to solve trigonometric identities problems step by step online. Prove the trigonometric identity (1+sin(x))(1-sin(x))=cos(x)^2. Starting from the left-hand side (LHS) of the identity. The sum of two terms multiplied by their difference is equal to the square of the first term minus the square of the second term. In other words: (a+b)(a-b)=a^2-b^2.. Apply the trigonometric identity: 1-\sin\left(\theta \right)^2=\cos\left(\theta \right)^2. Since we have reached the expression of our goal, we have proven the identity.

Final answer to the problem

true

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

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

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Prove the identity

$\left(1+sinx\right)\left(1-sinx\right)=cos^2x$

Prove the identity

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

Prove the identity

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

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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