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 + tan²θ.

Answer 1

4 sin² θ – 1 = 0

sin² θ = `(1)/(4)`

sin θ = `(1)/(2)`

sin θ = sin30°

θ = 30°

cos² θ + tan² θ= cos²30° + tan²30° 

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

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

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

= `(13)/(12)`