Let x be an acute angle such that \tan x + \sec x = 0. Find $\cos x$.
tanx + sec x = 0
sin x / cos x + 1 / cos x = 0
sin x / cos x = -1 / cos x square both sides
sin^2 x / cos^2x = 1 / cos^2 x
[ 1 - cos ^2 x ] / cos ^2 x = 1/ cos^2 x
1/ cos ^2 x - 1 = 1/ cos^2 x
-1 = 0 → no solution
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