Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The greatest and least values of (sin –1 x) 3 + (cos –1 x) 3 are-
Text Solution
Verified by ExpertsThe correct answer is:
3
(a, c)
Let y = (sin –1 x) 3 + (cos –1 x) 3 = (sin
–1 x + cos –1 x) ((sin –1 x) 2 + (cos –1 x) 2 –sin –1 x . cos –1 x)
Since –1 ≤ sin –1 x ≤ 1
or – 
≤ x ≤ π /2
y – π /2 = 
…(1)
y π /2 = 
…(2)
and 3(sin –1 x) 2 – 
sin –1 x + 
= 
⇒ 3(sin –1 x) 2 – 
sin –1 x + 
– 
= 0
for real, B 2 – 4AC ≥ 0
∴ 
– 4.3 . 
≥ 0
⇒ 
– 3 π 2 + 
≥ 0 ⇒ 
∴ y ≥ 
…(3)
From (1), (2) and (3)
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