The number of solutions of the equation ^ 2 ( sin x + 3) = 1 in [0,3π]is equal to

Correct answer: C. 6 ^ 2 (sin x + 3) = 1 = ^ 2 (π)/(4) ⇒ sin x + 3 = nπ ± (π)/(4) Also, 2 ≤ sin x + 3 ≤ 4 ⇒ sin x + 3 = π - (π)/(4), π + (π)/(4) ⇒ sin x = (3π)/(4) - 3 or (5π)/(4) - 3

NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

The number of solutions of the equation ^ 2 ( sin x + 3) = 1 in...

The number of solutions of the equation

\cot^{2} \left(

sin x + 3\right) = 1

in \left[0,3\pi\right]is equal to

The number of solutions of the equation ^ 2 ( sin x + 3) = 1 in [0,3π]is equal to

Options

A $2$
B $4$
C $6$
D $8$

Correct answer

C. $6$

Step-by-step solution

\cot^{2} \left(sin x + 3\right) = 1 = \cot^{2} \dfrac{\pi}{4}

⇒ sin x + 3 = n\pi \pm \dfrac{\pi}{4}

Also,

2 \le sin x + 3 \le 4

⇒ sin x + 3 = \pi - \dfrac{\pi}{4}, \pi + \dfrac{\pi}{4}

⇒ sin x = \dfrac{3\pi}{4} - 3

\dfrac{5\pi}{4} - 3

Practice Trigonometric Equations on Quantrex Academy →

More from Trigonometric Equations

Match each entry in List-I to the correct entry in List-II and choose the correct option.… JEE Advanced 2026 Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2… JEE Advanced 2026 Let S = \ θ ∈ (-2π, 2π) : θ + 1 = 3 θ\ . Then ∑_ θ ∈ S θ is equal to: JEE Main 2026 If S = \ θ ∈ [-π, π] : θ (5θ)/(2) = 7θ (7θ)/(2)\ , then n(S) is equal to _______. JEE Main 2026 Let S = \ x ∈ [-π, π] : x ( x + x) = a, a ∈ ℤ\ . Then n(S) is equal to : JEE Main 2026 The number of elements in the set \ x ∈[0,180^ ∘ ]: (x+100^ ∘ )= (x+50^ ∘ ) x (x-50^ ∘ )\… JEE Main 2026 Number of solutions of 3 2 θ+8 θ+3 3 =0, θ ∈[-3 π, 2 π] is: JEE Main 2026 The number of solutions of the equation 2 θ (θ)/(2)+ (5 θ)/(2)=2 ^3 (5 θ)/(2) in… JEE Main 2025 If for θ ∈[-(π)/(3), 0] , the points (x, y)=(3 (θ+(π)/(3)), 2 (θ+(π)/(6))) lie on x y+α… JEE Main 2025 If 10 ^4 θ+15 ^4 θ=6 , then the value of 27 cosec^6 θ+8 ^6 θ 16 ^8 θ is: JEE Main 2025 The number of solutions of equation (4- 3 ) x -2 3 ^2 x=- 4 1+ 3 , x ∈[-2 π, (5 π)/(2)] is JEE Main 2025 The number of solutions of the equation 2 x+3 x=π, x ∈[-2 π, 2 π]-\ ± (π)/(2), ± (3… JEE Main 2025 If θ ∈[-(7 π)/(6), (4 π)/(3)] , then the number of solutions of 3 cosec^2 θ-2( 3 -1)… JEE Main 2025 If θ ∈[-2 π, 2 π] , then the number of solutions of 2 2 ^2 θ+(2- 6 ) θ- 3 =0 , is equal… JEE Main 2025 The sum of all values of θ ∈[0,2 π] satisfying 2 ^2 θ= 2 θ and 2 ^2 θ=3 θ is JEE Main 2025 Let f: ℝ arrow ℝ be a function defined by f(x)=\ array cc x^2 ((π)/(x^2)), & if x ≠ 0 0… JEE Advanced 2024 Full Trigonometric Equations list Trigonometric Equations JEE Maths PYQs JEE Mathematics PYQs All NTA Abhyas JEE Main PYQs