Question

f sin^–1 (x – 3) + cos^–1(x – 1) + tan^–1= cos^–1 k – p then value of k is

• A. $\frac { 1 } { \sqrt { 2 } }$
• B. $- \frac { 1 } { \sqrt { 2 } }$
• C. 1
• D. – 1

Answer 1

Answer: (A)

$\frac { 1 } { \sqrt { 2 } }$

Answer 2

Sol. Q – 1 £ x – 3 £ 1

Ž 2 £ x £ 4 .………(i)

Also – 1 £ x – 1 £ 1

0 £ x £ 2 ………(ii)

form (i) & (ii) x = 2

Also, 2 – x² ¹ 0

x ¹ ± $\sqrt { 2 }$

\ At x = 2

sin^–1(2–3) + cos^–1(2–1) + tan^–1$\left( \frac { 2 } { 2 - 4 } \right)$= cos^–1k – p

$- \frac { \pi } { 2 }$+ 0 $- \frac { \pi } { 4 }$ = cos^–1 k – p

Ž cos^–1 k = p/4

Ž k = $\frac { 1 } { \sqrt { 2 } }$