Exams › JEE Main › Maths

If tan²(theta) + sec(theta) = 5, find the possible value(s) of cos(theta).

1. cos(theta) = 1/2 or cos(theta) = -1/3
2. cos(theta) = 1/3 or cos(theta) = -1/2
3. cos(theta) = 1/4 or cos(theta) = -1/3
4. cos(theta) = 1/2 only

Correct answer: cos(theta) = 1/2 or cos(theta) = -1/3

Solution

Using tan² = sec² - 1 gives sec² + sec - 6 = 0, so sec = 2 or sec = -3, i.e. cos = 1/2 or cos = -1/3.

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 →