Prove the trigonometric identity $\cos\left(a\right)^4-\sin\left(a\right)^4=\cos\left(2a\right)$

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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

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$\cos\left(a\right)^4-\sin\left(a\right)^4$

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Learn how to solve special products problems step by step online. Prove the trigonometric identity cos(a)^4-sin(a)^4=cos(2a). Starting from the left-hand side (LHS) of the identity. Simplify \sqrt{\cos\left(a\right)^4} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 4 and n equals \frac{1}{2}. Any expression multiplied by 1 is equal to itself. Simplify \sqrt{\sin\left(a\right)^4} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 4 and n equals \frac{1}{2}.

Final answer to the problem

true

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Function Plot

Plotting: $true$

Main Topic: Special Products

Special products is the multiplication of algebraic expressions that follow certain rules and patterns, so you can predict the result without necessarily doing the multiplication.

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