Question

$\sec(x) + \tan(x) = 3 \: { 0 < x < \frac{\pi}{2}$
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Answer 1

secx + tanx = 3

secx = 3 – tanx

sec²x = 9 + tan²x – 6tanx

sec²x - tan²x =9 – 6tanx

1 = 9 – 6tanx

3tanx = 4

x = tan⁻¹(3/4)

∴ x ≈ 37°

∴ x ∈ (0, π/2)