Question

If $a < \frac { 1 } { 32 }$ then the number of solution of$\left( \sin ^ { - 1 } x \right) ^ { 3 } + \left( \cos ^ { - 1 } x \right) ^ { 3 } = a \pi ^ { 3 }$ is.

• A. 0
• B. 1
• C. 2
• D. Infinite

Answer 1

Answer: (A)

0

Answer 2

From previous solution $\frac { \pi ^ { 3 } } { 32 } \leq \left( \sin ^ { - 1 } x \right) ^ { 3 } + \left( \cos ^ { - 1 } x \right) ^ { 3 } \leq \frac { 7 \pi } { 8 }$

Here $a < \frac { 1 } { 32 }$. So, number of solution is zero.