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Simplifying the Expression: 2πJ(1+(e−J3))=2\pi J\left(1+\left(\frac{e^{-J}}{3}\right)\right)=

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Csc, sec, and cot of special anglesright chevron icon

Full solution

Q. Simplifying the Expression: 2πJ(1+(e−J3))=2\pi J\left(1+\left(\frac{e^{-J}}{3}\right)\right)=
  1. Distribute 2πJ2\pi J: First, distribute 2πJ2\pi J to both terms inside the parentheses.\newline2πJ×1+2πJ×e−J32\pi J \times 1 + 2\pi J \times \frac{e^{-J}}{3}
  2. Simplify first term: Now, simplify the first term. 2πJ2\pi J
  3. Simplify second term: Next, simplify the second term. \newline(2πJ⋅e−J3)(\frac{2\pi J \cdot e^{-J}}{3})
  4. Combine terms: Combine both terms. 2πJ+2πJ⋅e−J32\pi J + \frac{2\pi J \cdot e^{-J}}{3}
  5. Correct mistake: Realize that I made a mistake in the distribution step; I forgot to multiply the JJ in the second term.

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