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

medium

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

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SIMILAR QUESTIONS

Q1

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

(cos α_n) = 1 is

easy View solution

Q2

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

medium View solution

Q3

diffcult View solution

Q4

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

easy View solution

Q5

is independent of θ, then

easy View solution

Q6

easy View solution

Q7

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

easy View solution

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

easy View solution

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

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Q10

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

easy View solution