Question

If x > 0, y > 0 and x > y, then

tan^–1 (x/y) + tan^–1 [(x + y)/(x – y)] is equal to-

• A. –p/4
• B. p/4
• C. 3p/4
• D. None of these

Answer 1

Answer: (C)

3p/4

Answer 2

Since $\frac{x}{y}.\frac{x + y}{x - y}$ > 1 .The given expression is equal to

p + tan^–1 $\left\lbrack \frac{\frac{x}{y} + \frac{x + y}{x - y}}{1 - \frac{x}{y} \times \frac{x + y}{x - y}} \right\rbrack$

= p + tan^–1 $\frac{x^{2} + y^{2}}{- (x^{2} + y^{2})}$ = p + tan^–1 (–1) = 3p/4.