JEE Maths›Trigonometric Functions›Question Types

Trigonometric Functions - How It Appears in JEE

8 recurring patterns. Learn the pattern, recognize it in 5 seconds, apply the right approach.

Simplify Compound Angle Expression

Pattern

Simplify or evaluate expressions involving sin(A+B), cos(A-B), tan(A+B)

How to recognize

Expression contains sin(A+B), cos(75), tan(15), or asks to simplify a sum/difference of trig values

→ Expand using compound angle formulas. Substitute known values. Look for cancellations or standard angles (15, 75, etc.).

Prove Trigonometric Identity

Pattern

Show that LHS = RHS using trig identities

How to recognize

Question says 'prove that', 'show that', or 'verify the identity'

→ Work on the more complicated side. Convert everything to sin and cos. Use sum-to-product or product-to-sum as needed. Factor and simplify.

Find General Solution of Trig Equation

Pattern

Solve trigonometric equations and express the general solution

How to recognize

Question asks to 'solve', 'find all values of x', or 'find the general solution'

→ Reduce to basic form (sin x = k, cos x = k, or tan x = k). Apply the standard general solution formula. Check for extraneous solutions if you squared or multiplied.

Maximum/Minimum of Trig Expression

Pattern

Find the maximum or minimum value of a trigonometric expression

How to recognize

Question asks 'max value of', 'min value of', 'range of' a trig expression

→ Write a sin x + b cos x = sqrt(a^2 + b^2) sin(x + phi). Range is [-sqrt(a^2+b^2), sqrt(a^2+b^2)]. For other forms, use AM-GM or calculus.

Properties of Triangle

Pattern

Find sides, angles, area, circumradius, or inradius of a triangle

How to recognize

Question involves a triangle with given sides/angles, asks for area, R, r, or other elements

→ Identify what is given (SSS, SAS, ASA). Apply sine rule, cosine rule, or area formula as appropriate. Use R = a/(2 sin A) and r = Delta/s.

Trig Series (Telescoping/Product)

Pattern

Evaluate a sum or product of trig terms, often telescoping

How to recognize

Summation of sin(k*theta), cos(k*theta), product of cos terms, or series with pattern

→ Multiply by a clever factor (e.g., 2 sin(d/2) for arithmetic angle series). Use product-to-sum to create telescoping. Known results: sum of sin AP, sum of cos AP.

Inverse Trig Composition/Simplification

Pattern

Simplify expressions like sin(cos^{-1} x), tan^{-1} a + tan^{-1} b

How to recognize

Expression involves sin^{-1}, cos^{-1}, tan^{-1} composed with trig functions or added together

→ Draw a right triangle for compositions. For tan^{-1} a + tan^{-1} b, use the addition formula: tan^{-1}((a+b)/(1-ab)) with correct quadrant adjustment.

Conditional Identity (A+B+C = pi)

Pattern

Given A+B+C = pi (triangle), prove a trig identity

How to recognize

Question states 'if A+B+C = pi' or 'in a triangle ABC, prove that'

→ Use A+B = pi - C to convert. Common tricks: sin(A+B) = sin C, cos(A+B) = -cos C. Convert sums to products. Standard results like sum of tan A = product of tan A.

←

Definite & Indefinite Integrals

Limits, Continuity & Differentiability

→