Exams › JEE Main › Maths

For which values of a does the equation sin⁴ x + cos⁴ x = a admit at least one solution?

1. for every real value of a
2. only when a = -1
3. only when a = 1/2
4. when 1/2 ≤ a ≤ 1

Correct answer: when 1/2 ≤ a ≤ 1

Solution

The expression sin⁴ x + cos⁴ x can be rewritten using the identity sin² x + cos² x = 1, leading to a maximum value of 1 and a minimum value of 1/2. Therefore, the equation admits solutions only for values of a within the range 1/2 to 1.

Related JEE Main Maths questions

• Find the period of the function |sin³(x/2)| + |cos⁵(x/5)|.
• 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)).
• If sin A - √(6)cos A = √(7)cos A, then the value of cos A + √(6)sin A is:

⚔️ Practice JEE Main Maths free + battle 1v1 →