Question

If n ĪN, and the set of equations cos^–1x + (sin^–1 y)² =$\frac { \mathrm { n } \pi ^ { 2 } } { 4 }$and (sin^–1y)² – cos^–1x = $\frac { \pi ^ { 2 } } { 16 }$ is consistent then n can be equal to–

• A. 0
• B. 1
• C. 3
• D. 4

Answer 1

Answer: (B)

1

Answer 2

Adding both equation we get

(sin^–1 y)² = $\left( \frac { 4 n + 1 } { 32 } \right)$ p²

Ž 0 £ p² £ $\frac { \pi ^ { 2 } } { 4 }$

Ž – $\frac { 1 } { 4 }$ £ n £ $\frac { 7 } { 8 }$

Also cos^–1 x = p²

Ž 0 £ $\frac { 4 \mathrm { n } - 1 } { 32 } \pi ^ { 2 } \leq \pi$

Ž $\frac { 1 } { 4 }$ £ n £ $\frac { 8 } { \pi }$+ 1.