Published by:
CGP EDU Academic Team
Published on: August 14, 2026
The number of real solutions of the equation
sin –1 
= 
– cos –1 
lying in the interval 
is __________.
(Here, the inverse trigonometric functions sin –1 x and cos –1 x assume values in 
and [0, π ], respectively).
Text Solution
Verified by ExpertsThe correct answer is:
2
(2)
Sol. sin –1 
= 
– cos –1 
= 
= 
or x = 0
⇒ x 3 + 2x 2 + 5x – 2 = 0
Let f(x) = x 3 + 2x 2 + 5x – 2
f '(x) > 0
f(0) = –2 and f(1/2) = 9/8 so one root in 
⇒ 2 roots
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