Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Trigonometric Equations

NTA Abhyas 2020 · Mathematics · Trigonometric Equations

General solution of the equation tan^ 2 θ + 2θ = 1 is

General solution of the equation tan2θ+sec⁡2θ=1tan^{2}\theta + \sec 2\theta = 1 is

Options

  1. Amπ,nπ+π3,m∈I,n∈Im\pi, n\pi + \dfrac{\pi}{3}, m \in I, n \in I
  2. Bmπ,nπ±π3,m∈I,n∈Im\pi, n\pi \pm \dfrac{\pi}{3}, m \in I, n \in I
  3. Cmπ,nπ±π6,m∈I,n∈Im\pi, n\pi \pm \dfrac{\pi}{6}, m \in I, n \in I
  4. DNone of these

Correct answer

B. mπ,nπ±π3,m∈I,n∈Im\pi, n\pi \pm \dfrac{\pi}{3}, m \in I, n \in I

Step-by-step solution

Using, sec⁡2θ=1cos⁡2θ=1+tan2θ1−tan2θ\sec 2\theta = \dfrac{1}{\cos 2\theta} = \dfrac{1 + tan^{2}\theta}{1 - tan^{2}\theta}

⇒⇒ We can write the given equation as tan2θ+1+tan2θ1−tan2θ=1tan^{2}\theta + \dfrac{1 + tan^{2}\theta}{1 - tan^{2}\theta} = 1

⇒tan2θ(1−tan2θ)+1+tan2θ=1−tan2θ⇒tan^{2}\theta ( 1 - tan^{2}\theta ) + 1 + tan^{2}\theta = 1 - tan^{2}\theta

⇒3tan2θ−tan4θ=0⇒tan2θ(3−tan2θ)=0⇒3tan^{2}\theta - tan^{4}\theta = 0 ⇒ tan^{2}\theta ( 3 - tan^{2}\theta ) = 0

⇒tanθ=0⇒tan\theta = 0 or tan⁡2θ=3=(3)2\tan^{2} \theta = 3 = {( \sqrt{3} )}^{2}

⇒tan \theta=0⇒\theta=m\pi,m∈I⇒ \text{tan \theta} = 0 ⇒ \text{\theta} = m\text{\pi ,}m \in I

or tan⁡2θ=tan⁡2π3⇒θ=nπ±π3\tan^{2} \theta = \tan^{2} \dfrac{π}{3}⇒ \theta = n\pi \pm \dfrac{\pi}{3}, n∈In \in I
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 2026Passage: Consider the curve C_1 given by y = e^ -x for x ∈ [0, 10π] , and the curve C_2… JEE Advanced 2026Let S = \ θ ∈ (-2π, 2π) : θ + 1 = 3 θ\ . Then ∑_ θ ∈ S θ is equal to: JEE Main 2026If S = \ θ ∈ [-π, π] : θ (5θ)/(2) = 7θ (7θ)/(2)\ , then n(S) is equal to _______. JEE Main 2026Let S = \ x ∈ [-π, π] : x ( x + x) = a, a ∈ ℤ\ . Then n(S) is equal to : JEE Main 2026The number of elements in the set \ x ∈[0,180^ ∘ ]: (x+100^ ∘ )= (x+50^ ∘ ) x (x-50^ ∘ )\… JEE Main 2026Number of solutions of 3 2 θ+8 θ+3 3 =0, θ ∈[-3 π, 2 π] is: JEE Main 2026The number of solutions of the equation 2 θ (θ)/(2)+ (5 θ)/(2)=2 ^3 (5 θ)/(2) in… JEE Main 2025If for θ ∈[-(π)/(3), 0] , the points (x, y)=(3 (θ+(π)/(3)), 2 (θ+(π)/(6))) lie on x y+α… JEE Main 2025If 10 ^4 θ+15 ^4 θ=6 , then the value of 27 cosec^6 θ+8 ^6 θ 16 ^8 θ is: JEE Main 2025The number of solutions of equation (4- 3 ) x -2 3 ^2 x=- 4 1+ 3 , x ∈[-2 π, (5 π)/(2)] is JEE Main 2025The number of solutions of the equation 2 x+3 x=π, x ∈[-2 π, 2 π]-\ ± (π)/(2), ± (3… JEE Main 2025If θ ∈[-(7 π)/(6), (4 π)/(3)] , then the number of solutions of 3 cosec^2 θ-2( 3 -1)… JEE Main 2025If θ ∈[-2 π, 2 π] , then the number of solutions of 2 2 ^2 θ+(2- 6 ) θ- 3 =0 , is equal… JEE Main 2025The sum of all values of θ ∈[0,2 π] satisfying 2 ^2 θ= 2 θ and 2 ^2 θ=3 θ is JEE Main 2025Let 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 PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs