Q1
What is the fundamental trigonometric identity?
Asin²θ + cos²θ = 1
Bsin θ + cos θ = 1
Csin²θ - cos²θ = 1
Dsin θ × cos θ = 1
ICSEClass 10 (ICSE)MathematicsCh 21 · Topic 1
Trigonometric Identities
Trigonometric identities are equations involving trigonometric functions that hold true for all angle values, useful for simplifying express
Core concept
The fundamental identity sin²θ + cos²θ = 1 relates sine and cosine, derived from the Pythagorean theorem applied to a right triangle.
How it works
Other identities include 1 + tan²θ = sec²θ and 1 + cot²θ = cosec²θ, derived from the fundamental identity.
Why it matters
These identities help simplify complex trigonometric expressions and solve trigonometric equations more efficiently.
Key detail
Understanding and applying trigonometric identities is essential for advanced trigonometry problems and proving trigonometric relationships.
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• Fundamental identity: sin²θ + cos²θ = 1.
• This comes from the Pythagorean theorem.
• 1 + tan²θ = sec²θ.
• 1 + cot²θ = cosec²θ.
• These derive from the fundamental identity.
• Identities simplify complex expressions.
• They help solve trigonometric equations.
• They're essential for advanced trigonometry.