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Popular >

simplify (e^{iθ}+e^{-iθ})^3

Solution

simplify

(e^{i θ} + e^{- i θ})^{3}

Solution

8 cos^{3} (θ)

Solution steps

(e^{i θ} + e^{- i θ})^{3}

e^{i θ} = cos (θ) + i sin (θ)

e^{- i θ} = cos (θ) - i sin (θ)

= (cos (θ) + i sin (θ) + cos (θ) - i sin (θ))^{3}

Simplify

cos (θ) + sin (θ) i + cos (θ) - i sin (θ) : 2 cos (θ)

= (2 cos (θ))^{3}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 2^{3} cos^{3} (θ)

2^{3} = 8

= 8 cos^{3} (θ)

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Frequently Asked Questions (FAQ)

What is (e^{iθ}+e^{-iθ})^3 ?
The solution to (e^{iθ}+e^{-iθ})^3 is 8cos^3(θ)