Question

The equation sin4 x + cos4 x = a has a real solution for

Solution

Correct option is

a = 7/10

     

 

 

 

 

     

 

From (1) and (2) we get 1/2 ≤ a ≤ 1.

Note that a = 1/2 for x = π/4 and a = 1 for x = π/2.

SIMILAR QUESTIONS

Q1

If αβ are positive acute angles and  then tan α = k tanβ such that

Q2
Q4

The maximum value of (cos α1) (cos α2) …(cos αn) under the restriction 0 ≤ α1, α1,…., α1 ≤ π/2 and (cos α1) (cos α2) …

(cos αn) = 1 is

Q5

The number of integral values of k for which the equation 7 cos x + 5 sin x = 2k + 1 has a solution is

 

Q6

 

                                                              

Q7

  

    

are two matrices such that AB is the null matrix, then

Q8

 is independent of θ, then

Q10

If sin θ (1 + sin θ) + cos θ (1 + cos θ) = x and sin θ (1 – sin θ) + cos θ (1 – cos θ) = y then