Question

If 4 sin² θ – 1 = 0 and angle θ is less than 90°, find the value of θ and hence the value of cos² θ + tan² θ.

Answer 1

4 sin² θ – 1 = 0

sin² θ = `(1)/(4)`

sin θ = `(1)/(2)`

sin θ = sin 30°

θ = 30°

cos² θ + tan² θ = cos² 30° + tan² 30° 

= `(sqrt(3)/2)^2 + ( 1/sqrt(3))^2`

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

= `(9 + 4)/(12)`

= `(13)/(12)`