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Question: The equation (sin<sup>–1</sup>x)<sup>3</sup> + (cos<sup>–1</sup>x)<sup>3</sup> = ap<sup>3</sup> has ...

The equation (sin–1x)3 + (cos–1x)3 = ap3 has no solution for

A

a> 132\frac { 1 } { 32 }

B

a = 132\frac { 1 } { 32 }

C

a< 1

D

a< 132\frac { 1 } { 32 }

Answer

a< 132\frac { 1 } { 32 }

Explanation

Solution

Maximum value of (sin–1x + cos–1x)3 = 7π38\frac { 7 \pi ^ { 3 } } { 8 }

Minimum value = π332\frac { \pi ^ { 3 } } { 32 }

So a ≮\nless 132\frac { 1 } { 32 }