Exams › JEE Advanced › Maths

Given sin(alpha) = 3/5 and cos(beta) = 9/41 (both alpha and beta in the first quadrant), find sin(alpha - beta) and cos(alpha + beta).

1. sin(alpha - beta) = -133/205; cos(alpha + beta) = -84/205
2. sin(alpha - beta) = 133/205; cos(alpha + beta) = 84/205
3. sin(alpha - beta) = -84/205; cos(alpha + beta) = -133/205
4. sin(alpha - beta) = 133/205; cos(alpha + beta) = -84/205

Correct answer: sin(alpha - beta) = -133/205; cos(alpha + beta) = -84/205

Solution

With cos(alpha) = 4/5 and sin(beta) = 40/41, the addition formulas give sin(alpha - beta) = -133/205 and cos(alpha + beta) = -84/205.

Related JEE Advanced Maths questions

• Identify the periodic function among the following:
• Given that α, β, γ, and θ are the smallest positive angles in increasing order for which their sine values equal a positive constant k, what is the result of 4 sin(α/2) + 3 sin(β/2) + 2 sin(γ/2) + sin(θ/2)?
• Consider the function fn(θ) = tan(θ/2)(1 + sec²θ)(1 + sec⁴θ)... (1 + sec²ⁿθ). Which of the following is true?
• Given that (a−b)sin(θ+ϕ) = (a+b)sin(θ−ϕ) and a tan(θ/2) − b tan(ϕ/2) = c, which of the following holds true?
• In a right-angled triangle ABC where ∠B = 90° and the sum of the two legs a and b equals 4, the triangle's area is maximized when ∠C is:
• If the altitudes p₁, p₂, and p₃ of a triangle enclose a circle with a diameter of 4/3 units, what is the minimum possible value of p₁ + p₂ + p₃?

⚔️ Practice JEE Advanced Maths free + battle 1v1 →