Question

From the following figure, find:
(i) y
(ii) sin x°
(iii) (sec x° - tan x°) (sec x° + tan x°)

Answer 1

Consider the given figure :

(i) Since the triangle is a right-angled triangle, so using Pythagorean Theorem
2² = y² + 1²
y² = 4 – 1 = 3
y = `sqrt3` 

(ii) sin x° = `"perpendicular"/"hypotenuse" =  (sqrt3)/(2)`

(iii) tan x° = `"perpendicular"/"base" = sqrt3`

     sec x° = `"hypotenuse"/"base" = 2`

Therefore
( sec x° – tan x°) ( sec x° + tan x°)

= (2–`sqrt3`) (2+`sqrt3`)

= 4 – 3

= 1