Trigonometry

Board: JEE Advanced | Exam: JEE Advanced

JEE Advanced study notes for Trigonometry by Ajay Yadav. In-depth coverage of advanced topics and problem-solving techniques.

Key Concepts

Compound and Multiple Angles

Formulas for 2A, 3A, 4A. sin18°, cos36° values. Series: sinα+sin(α+β)+…

Inverse Trigonometry

Property proofs. Sum of series involving inverse trig functions. Simplification using substitution: x=tanθ, x=sinθ, etc.

Trigonometric Equations

General solutions. Equations using transformations. Equations with parameter. Maximum/minimum of trig expressions: asinθ+bcosθ → range (-&radic(a&sup2+b&sup2),&radic(a&sup2+b&sup2))

Properties of Triangles

Sine rule: a/sinA=b/sinB=c/sinC. Cosine rule: a²=b²+c²-2bccosA. Projection formulas. Napier’s analogy. Area: Δ=abc/4R=rs=√[s(s-a)(s-b)(s-c)].

Important Formulas

a sinθ+b cosθ	R sin(θ+φ), R=√a²+b²
Sine rule	a/sinA = 2R
Cosine rule	a²=b²+c²-2bccosA
Area	Δ = rs = abc/4R

Solved Examples

Example 1: Find maximum of sinθ+cosθ.

Solution: R=√1+1=√2. Max = √2.

Practice Questions

1. Find sin18°.
2. Solve: 2sin²θ+sinθ-1=0.
3. Prove sin⁻¹(3/5)+sin⁻¹(8/17)=sin⁻¹(77/85).
4. In ΔABC, prove a=bcosC+ccosB.
5. Find area of triangle with sides 13,14,15.

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