Question

If f(x) = sin^–1 x + cos^–1 x + tan^–1 x + cot^–1 x + sec ^–1 x, then

f(x) lies in the interval-

• A. [p, 2p]
• B. (p, 2p)
• C. $\left( \frac { 3 \pi } { 2 } , 2 \pi \right]$
• D. None of these

Answer 1

Answer: (C)

$\left( \frac { 3 \pi } { 2 } , 2 \pi \right]$

Answer 2

f(x) = $\frac { \pi } { 2 }$+$\frac { \pi } { 2 }$ + sec^–1 x

But 0 £ sec^–1 x £ p, sec^–1 x ¹ $\frac { \pi } { 2 }$

\ p £ f(x) £ 2p, f(x) ¹ $\frac { 3 \pi } { 2 }$.