Trigonometry
9 solved problems from JEE previous year papers.
Properties of Triangles
Find the length of the median from vertex A to side BC in a triangle with AB=8cm, AC=6cm and angle BAC=60°, using the cosine rule…
Trigonometric Identities
If A + B + C = 180°, Prove That sin 2A + sin 2B − sin 2C = 4 cos A cos B sin C
Prove that sin2A+sin2B−sin2C=4cosA cosB sinC when A+B+C=180°, using the sum-to-product formula twice along with the…
Trigonometric Identities
The Value of cos(π/2²)·cos(π/2³)⋯cos(π/2¹⁰)·sin(π/2¹⁰) Is
Find the value of the product cos(π/4)cos(π/8)···cos(π/1024)sin(π/1024) using the repeated identity sinθcosθ=½sin2θ to telescope…
Inverse Trigonometric Functions
Express tan⁻¹(cos x/(1 − sin x)), Where x ∈ (−3π/2, π/2), in Its Simplest Form
Simplify tan⁻¹(cosx/(1−sinx)) for x∈(−3π/2,π/2) using half-angle substitutions to reveal it equals tan(π/4+x/2), matching the…
Trigonometric Functions
cot x = −5/√11, x∈(π/2,π) — Evaluate a Multi-Angle Trig Expression
Given cot x = −5/√11 with x in the second quadrant, evaluate (sin(11x/2))(sin6x−cos6x)+(cos(11x/2))(sin6x+cos6x) by collapsing it…
Trigonometric Functions
A Wheel Makes 360 Revolutions in 1 Minute. Find the Number of Radians It Turns Through in 1 Second
A wheel makes 360 revolutions in one minute. Find how many radians it turns through in 1 second, converting revolutions per…
Trigonometric Functions
The Value of 2sin(12°) − sin(72°)
Evaluate 2sin(12°)−sin(72°) by splitting 72° as 60°+12°, then recombining into a single sine of a difference angle using sin18°.
Trigonometric Functions
Given sinx+sin²x=1 for x in (0,π/2), evaluate a large trigonometric expression by first proving tanx=cosx, then spotting a…
Inverse Trigonometric Functions
If sec²(tan⁻¹α) + cosec²(cot⁻¹β) = 36 and α + β = 8 With α < β, Then α² + β Is
Given sec²(tan⁻¹α)+cosec²(cot⁻¹β)=36 and α+β=8 with α