Exams › JEE Main › Maths

Which of the following trigonometric identities is correct?

1. (sin 2A + sin 2B)/(sin 2A - sin 2B) = tan(A + B)/tan(A - B)
2. (cos 2B + cos 2A)/(cos 2B - cos 2A) = cot(A + B) cot(A - B)
3. cos(A + B) + sin(A - B) = 2 sin(45 deg + A) cos(45 deg + B)
4. (sin 7θ - sin 5θ)/(cos 7θ + cos 5θ) = tan θ

Correct answer: (sin 2A + sin 2B)/(sin 2A - sin 2B) = tan(A + B)/tan(A - B)

Solution

Using sum-to-product, the ratio simplifies to [sin(A+B)cos(A-B)]/[cos(A+B)sin(A-B)] = tan(A+B)/tan(A-B), so option (a) is the valid identity.

Related JEE Main Maths questions

• Find the period of the function |sin³(x/2)| + |cos⁵(x/5)|.
• For which values of a does the equation sin⁴ x + cos⁴ x = a admit at least one solution?
• For n ∈ N, let fₙ(θ)=tan ((θ)/(2)) (1+secθ)(1+sec 2θ)(1+sec 4θ)⋯(1+sec 2ⁿθ). Which of the following is true?
• Simplify the following expression: (cos 6x + 6cos 4x + 15cos 2x + 10)/(cos 5x + 5cos 3x + 10cos x). What does it equal?
• For angles α, β, γ all lying in the interval (0, π/2), the value of (sin(α+β+γ))/(sinα+sinβ+sinγ) is
• Evaluate the product (1 + cos(π/10))(1 + cos(3π/10))(1 + cos(7π/10))(1 + cos(9π/10)).

⚔️ Practice JEE Main Maths free + battle 1v1 →