Question

If 4 cos² x° - 1 = 0 and 0 ∠ x° ∠ 90°,
find:(i) x°
(ii) sin² x° + cos² x°
(iii) `(1)/(cos^2xx°) – (tan^2 xx°)`

Answer 1

(i) 4 cos²x° – 1 = 0
4 cos²x° = 1

co^s2x° = `(1/2)^2`

cosx° = `(1)/(2)`

cosx° = cos60°

x° = 60°

(ii) sin² x° + cos²x° = sin²60° + cos²60°

= `(sqrt3/2)^2 + (1/2)^2`

= `(3)/(4) + (1)/(4)`

= 1

(iii) `(1)/(cos^2xx°) – tan^2xx° = (1)/cos^260° – tan^2 60°`

= `(1)/(1/2)^2 – (sqrt3)^2`

= 4 – 3

= 1