Question

From the given figure,
find:
(i) cos x°
(ii) x°
(iii) `(1)/(tan^2 xx°) – (1)/(sin^2xx°)` 
(iv) Use tan x^o, to find the value of y.

Answer 1

(i) cos x° = `(10)/(20)`

cos x° = `(1)/(2)`

 

(ii) cos x° = `(1)/(2)`

cos x° = cos 60°

x° = 60°

 

(iii)  `(1)/(tan^2x°) – (1)/(sin^2x°) = (1)/(tan^2 60°) – (1)/(sin^2 60°)`

= `(1)/(sqrt3)^2 – (1)/(sqrt3/2)^2`

= `(1)/(3) – (4)/(3)`

= – 1

(iv) tan x° = tan 60°
= `sqrt3`

We know that tan x° = `"AB"/"BC"`

⇒ tan x° = `"y"/(10)`

⇒ y = 10 tan x°
⇒ y = 10 tan 60°
⇒ y = 10`sqrt3`