# Lesson Worksheet: Euler’s Formula for Trigonometric Identities Mathematics

In this worksheet, we will practice using Euler’s formula to prove trigonometric identities like double angle and half angle.

**Q1: **

Use Eulerโs formula to express in terms of .

*Hint*: First write and in terms of and .

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**Q2: **

Using Eulerโs formula, express in terms of .

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**Q3: **

Using Eulerโs formula, derive a formula for and in terms of and .

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**Q4: **

Using Eulerโs formula, express in the form , where , , and are constants to be found.

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**Q5: **

Express and in terms of and .

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**Q6: **

Using Eulerโs formula, express in the form , where , , and are constants to be found.

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**Q7: **

Using Eulerโs formula, express in terms of sine and cosine.

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**Q8: **

What trigonometric identities can be derived by applying Eulerโs identity to ?

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**Q9: **

Use Eulerโs formula to express in terms of sine and cosine.

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Given that , what trigonometric identity can be derived by expanding the exponentials in terms of trigonometric functions?

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**Q10: **

Use Eulerโs formula to derive a formula for and in terms of and .

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Hence, express in terms of .

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