The number of solutions of the equation sin- 1x=(sin x)- 1 is/are

Question

The number of solutions of the equation sin- 1x=(sin x)- 1 is/are (A) one (B) two (C) three (D) zero

Tardigrade Admin · Accepted Answer

∵ (sin x)- 1=(1/sin â¡ x)=cosec â¡ x Now, from graphs of sin- 1 x ,cosec â¡ x <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-dtpqt0dj1pca.png" /> Clearly, both graph intersects at two points ∴ two solutions

Q. The number of solutions of the equation $s i n^{- 1} x = (s in x)^{- 1}$ is/are

one

two

three

zero

$∵ (s in x)^{- 1} = \frac{1}{s in x} = cosec x$
Now, from graphs of $s i n^{- 1} x, cosec x$

Clearly, both graph intersects at two points
$∴$ two solutions

Q. The number of solutions of the equation sin−1x=(sinx)−1 is/are

one

two

three

zero

∵(sinx)−1=sin⁡x1​=cosec⁡x Now, from graphs of sin−1x,cosec⁡x Clearly, both graph intersects at two points ∴ two solutions

Q. The number of solutions of the equation $s i n^{- 1} x = (s in x)^{- 1}$ is/are

$∵ (s in x)^{- 1} = \frac{1}{s in x} = cosec x$
Now, from graphs of $s i n^{- 1} x, cosec x$

Clearly, both graph intersects at two points
$∴$ two solutions