Question

If sin 3A = 1 and 0 < A < 90^°, find `tan^2A - (1)/(cos^2 "A")`

Answer 1

sin 3A = 1 
sin 3A = sin90°
3A = 90°
A = 30°

`tan^2A – (1)/(cos^2"A") = tan^2 30° – (1)/(cos^2 30°)`

= `(1/sqrt3)^2 – (1)/(sqrt3/2)^2`

= `(1)/(3) – (4)/(3)`

= `(–3)/(3)`

= – 1