Question
Question: The number of solution of equation p cot<sup>–1</sup>(x–1) + (p–1) cot<sup>–1</sup>x = 2p – 1...
The number of solution of equation
p cot–1(x–1) + (p–1) cot–1x = 2p – 1
A
0
B
1
C
2
D
3
Answer
1
Explanation
Solution
Let f(x) = p cot–1(x–1) + (p – 1) cot–1 x
f ¢(x) = 
< 0 ∀ xĪR
Hence f(x) is decreasing function and 0 < f(x) < p (2p –1)
\ f(x) = 2p –1 has only one solution