Question

tangent square + cot square + 2

Answer 1

tan² x + cot² x = 2

=> tan² x + (1/ tan²x) = 2

=> tan^4 x + 1 = 2tan² x

=> tan^4x -2tan² x +1 = 0

=> ( tan²x -1) ² = 0 ( by algebraic identity)

=> ( tan x +1) ( tan x -1) ( tan x + 1 ) ( tan x-1) =0 ( by algebraic identity)

=> tan x = +1, —1

Since tan x is +ve in the 1st quadrant, —ve in the 2nd quadrant.

=> x= 45°, ( 180°- 45°)= 135°

=> x = 45°, 135° ……….ANS