The Values Of θ lying Between 0 And π/2 And Satisfying The Equation                       

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Question

The values of θ lying between 0 and π/2 and satisfying the equation

                      

Solution

Correct option is

7π/24 and 11π/24

Appling R1 → R1 – R3 and R2 → R2 – R3 on the L.H.S. the given equation can be written as

                    

Expanding the LHS along R1, we get 1 + 4 sin 4θ + cos2 θ + sin2 θ = 0   

 ∴ 4 sin 4θ = – 2 ⇒ sin 4θ = – 1/2

 ∴ 4θ = 7π/6 or 11π/6 

 [∴ 0 < θ < π/2 ⇒ 0 < 4θ  < 2π]

 ∴ θ = 7π/24 or 11π/24

Testing

SIMILAR QUESTIONS

Q1

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

Q2

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

 

Q3

 

                                                              

Q4

  

    

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

Q5

 is independent of θ, then

Q7

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

Q8

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

Q9

If sec A tan B + tan A sec B = 91, then the value of (sec A sec B + tan A tan B)2 is equal to

Q10

Find the maximum and minimum values of 6 sin x cos x + 4 cos 2x.