Question

If cosec x =√(10), find the value of tan x.

Answer 1

Answer:

1/3

Step-by-step explanation:

cosec x=√10

Using identity, 1+cot²x=cosec²x

cot²x= cosec²x-1

        = (√10)² -1

        = 10-1

        =9

cot x= √9 =3

tanx= 1/cot x =1/3

Answer 2

Step-by-step explanation:

cosec x = √10 = 1/sin x

therefore sin x = 1/√10

therefore perpendicular = 1x, hypotenuse = √10x and by Pythagoras theorem,

base = √ (√10x)² - (1x)²

=> base = √(10x² - x²)

=> base = √9x² => 3x

tan x = perpendicular / base

=> tan x = 1x/3x => 1/3