삼각방정식

$3 \cos 2 x + 17 \cos x = 0$ $3 ( 2 \cos ^{2} x - 1 ) + 17 \cos x = 0$ $\cos x = t ( - 1 \leq t \leq 1 )$로 치환하면 $6 t ^{2} + 17 t - 3 = 0$ $( t + 3 ) ( 6 t - 1 ) = 0$ $\displaystyle \therefore t = \cos x = \frac{1}{6} ( \because - 1 \leq t \leq 1 )$ $\tan ^{2} x = \sec ^{2} x - 1 = 36 - 1 = 35$