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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Inverse Trigonometric Functions

NTA Abhyas 2020 · Mathematics · Inverse Trigonometric Functions

The number of solutions of the equation sin^ - 1 x = (sin x) ^ - 1...

The number of solutions of the equation sin−1x=(sinx)−1sin^{- 1}x = {\left(sin x\right)}^{- 1} is/areThe number of solutions of the equation sin^ - 1 x = (sin x) ^ - 1 is/are

Options

  1. Aone
  2. Btwo
  3. Cthree
  4. Dzero

Correct answer

B. two

Step-by-step solution

∵(sinx)−1=1sinx=cosecx∵ {\left(sin x\right)}^{- 1} = \dfrac{1}{sin x} = cosec x
Now, from graphs of sin⁡−1x,cosecx\sin^{-1} x,cosec x
The number of solutions of the equation sin^ - 1 x = (sin x) ^ - 1 is/are
Clearly, both graph intersects at two points
∴∴ two solutions
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