Question

sin x + cos x = 1/2 then tan x =

Answer 1

$\sin(x) + \cos(x) = \frac{1}{2} \\ dividing \: throughout \: by \: \cos(x) \\ \tan(x) + 1 = \frac{ \sec(x) }{2} \\ squaring \: both \: sides \\ {( \tan(x) + 1) }^{2} = \frac{ { \sec}^{2}( x)}{4} \\ { \tan }^{2} (x) + 2 \tan(x) + 1 = \frac{1 + { \tan}^{2} x}{4} \\ 3{ \tan }^{2} (x) + 8 \tan(x) + 3 =0 \\ \tan(x) = \frac{ - 8 \: + \: \: or \: \: - \sqrt{ {8}^{2} - 4 \times 3 \times 3 } }{2 \times 3} \\ = - 4/3 + \sqrt{7}/3 \: \: \: or \: \: \: - 4/3 - \sqrt{7}/3$

Answer 2

Answer:

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