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Questions and Answers
What is the definition of sin(2x)?
What is the definition of sin(2x)?
What is one definition of cos(2x)?
What is one definition of cos(2x)?
What is the definition of tan(2x)?
What is the definition of tan(2x)?
2tanx / (1 - tan²x)
What is the definition of sin(x/2)?
What is the definition of sin(x/2)?
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What is the definition of cos(x/2)?
What is the definition of cos(x/2)?
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What is the definition of tan(x/2)?
What is the definition of tan(x/2)?
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Study Notes
Half Angle and Double Angle Identities
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sin(2x) is expressed as 2sinxcosx, representing the sine of double angles using the sine and cosine of the original angle.
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cos(2x) can be represented by various forms:
- cos²x - sin²x, demonstrating the relationship between squares of cosine and sine.
- 2cos²x - 1, allowing transformation using cosine.
- 1 - 2sin²x, providing an alternative expression based on sine.
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tan(2x) is calculated using the formula 2tanx / (1 - tan²x), offering a tangent double angle expression derived from the tangent of the original angle.
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For the half-angle identities:
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sin(x/2) can be expressed as ±√(1-cosx)/2, relating the sine of halved angles to the cosine.
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cos(x/2) is defined by ±√(1+cosx)/2, connecting the cosine of halved angles back to the original cosine value.
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tan(x/2) is determined by ±√(1-cosx)/(1+cosx), showing the tangent of half angles as a function of the cosine.
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These identities are crucial in trigonometry for simplifying expressions and solving equations.
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