AM-2471

Trigonometric equations

A Math · Secondary 4 · Hard · Trigonometric equations

Solve the equation

\tan x + 3\sec^2 x = 7

for

0 \le x \le 2\pi

$x = \dfrac{\pi}{4},\; \dfrac{5\pi}{4},\; \pi - \arctan\dfrac{4}{3},\; 2\pi - \arctan\dfrac{4}{3}$
$x = \dfrac{\pi}{4},\; \dfrac{5\pi}{4}$ only
$x = \arctan\dfrac{4}{3},\; \pi+\arctan\dfrac{4}{3}$
$x = \dfrac{\pi}{4},\; \dfrac{5\pi}{4},\; \arctan\dfrac{4}{3},\; \pi+\arctan\dfrac{4}{3}$

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