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

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The value of ^ -1 (cos ^ -1 x) + ^ -1 (sin ^ -1 x) is equal to

The value of sin⁡−1(cossin⁡−1x)+cos⁡−1(sincos⁡−1x)isequalto\sin^{-1} \left(cos \sin^{-1} x\right) + \cos^{-1} \left(sin \cos^{-1} x\right) is equal to

Options

  1. A00
  2. Bπ4\dfrac{\pi}{4}
  3. Cπ2\dfrac{\pi}{2}
  4. D3π4\dfrac{3\pi}{4}

Correct answer

C. π2\dfrac{\pi}{2}

Step-by-step solution

\sin^{-1} \left(cos \sin^{-1} x\right) = \dfrac{\pi}{2} - \cos^{-1}(cossin⁡−1x)\left(cos \sin^{-1} x\right)
=π2−sin⁡−1= \dfrac{\pi}{2} - \sin^{-1} x<br/>Similarly,cos⁡−1(sincos⁡−1x)=π2−cos⁡−1<br />Similarly, \cos^{-1} \left(sin \cos^{-1} x\right) = \dfrac{\pi}{2} - \cos^{-1} x<br/>Addingboth,weget,<br/></br/>sin⁡−1(cossin⁡−1x)+cos⁡−1(sincos⁡−1x)<br />Adding both, we get,<br /></br />\sin^{-1} \left(cos \sin^{-1} x\right) + \cos^{-1} \left(sin \cos^{-1} x\right)
=π−(sin⁡−1x+cos⁡−1x)= \pi - \left(\sin^{-1} x + \cos^{-1} x\right)
=π2= \dfrac{\pi}{2}
Practice Inverse Trigonometric Functions on Quantrex Academy →

More from Inverse Trigonometric Functions

Considering only the principal values of the inverse trigonometric functions, the value… JEE Advanced 2026Let α = 3 ^ -1 ((6)/(11)) and β = 3 ^ -1 ((4)/(9)) , where inverse trigonometric… JEE Main 2026If ( ^ -1 (x 2 )) = ( ^ -1 1-x^2 ) , x ∈ (0,1) , then the value of x is : JEE Main 2026Let [·] denote the greatest integer function. If the domain of the function f(x) = ^ -1… JEE Main 2026Let 0 < α < 1 , β = (1)/(3α) and ^ -1 (1-α) + ^ -1 (1-β) = (π)/(4) . Then 6(α + β) is… JEE Main 2026If (π)/(4) + ∑_ p=1 ^ 11 ^ -1 ( 2^ p-1 1 + 2^ 2p-1 ) = α , then α is equal to __________. JEE Main 2026If y = ^ -1 ((3 x - 4 x)/(4 x + 3 x)) + 2 ^ -1 ( x 1+ 1-x^2 ) , then (dy)/(dx) at x = 3 2… JEE Main 2026Considering the principal values of inverse trigonometric functions, the value of the… JEE Main 2026If k= ((π)/(4)+(1)/(2) ^ -1 ((2)/(3)))+ ((1)/(2) ^ -1 ((2)/(3))) , then the number of… JEE Main 2026If the domain of the function f(x)= ^ -1 ( 1 x^ 2 -2 x-2 ) , is (-∞, α] [β, γ] [δ, ∞)… JEE Main 2026The number of solutions of ^ -1 4x + ^ -1 6x = (π)/(6) , where - 1 2 6 < x < 1 2 6 , is… JEE Main 2026Let the maximum value of ( ^ -1 x)^ 2 +( ^ -1 x)^ 2 for x ∈[- 3 2 , 1 2 ] be m n π^ 2… JEE Main 2026If the domain of the function f(x)= ^ -1 ((2 x-5)/(11-3 x))+ ^ -1 (2 x^ 2 -3 x+1) is the… JEE Main 2026The total number of real solutions of the equation θ= ^ -1 (2 θ)-(1)/(2) ^ -1 ((6 θ)/(9+… JEE Advanced 2025The value of ^ -1 ( 1+ ^2(2) -1 (2) )- ^ -1 ( 1+ ^2((1)/(2)) +1 ((1)/(2)) ) is equal to JEE Main 2025The sum of the infinite series ^ -1 ((7)/(4))+ ^ -1 ((19)/(4))+ ^ -1 ((39)/(4))+ ^ -1… JEE Main 2025 Full Inverse Trigonometric Functions list Inverse Trigonometric Functions JEE Maths PYQsJEE Mathematics PYQs All NTA Abhyas JEE Main PYQs