If sin 3A = 1 and 0 < A < 90°, find tan 2 A − 1 cos 2 A

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

Sum

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

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Trigonometric Equation Problem and Solution

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