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