Q) The number of solution(s) of the equation tan-11+x+tan-11-x=π2 is (1) 3 (2) 2 (3) 1 (4) 4 - Maths - Inverse Trigonometric Functions

Question

Q) The number of solution(s) of the equation tan - 1 1 + x + tan -
1 1 - x = π 2 is
(1) 3
(2) 2
(3) 1
(4) 4

Aarushi Mishra · Accepted Answer

tan-11+x+tan-11-x=π2If we have angles A and B such thatA+B=π2Also tan A+B=tan A+tan B1-tan A tan B=tan π2=∞⇒1-tan A tan B=0tan A tan B=1HereA=tan-11+xB=tan-11-xtan tan-11+x tan tan-11-x=11+x1-x=11-x2=1x=0Hence we have only one solution

Q). The number of solution(s) of the equation tan - 1 1 + x + tan - 1 1 - x = π 2 is (1) 3 (2) 2 (3) 1 (4) 4

Q). The number of solution(s) of the equation $\tan^{- 1} (1 + x) + \tan^{- 1} (1 - x) = \frac{π}{2}$ is
(1) 3
(2) 2
(3) 1
(4) 4