If sin x+cos x=15 and 0≤ x<π, then tan x is

1978 AMC 12 Problem 15

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15.

\sin x+\cos x=\frac15

and

0\le x\lt\pi,

then

\tan x

-\frac43

-\frac34

\frac34

\frac43

not completely determined by the given information

Square the given equation to determine

\sin x\cos x

Treat

\sin x

and

\cos x

as roots of a quadratic, then use

0\le x\lt\pi

Squaring gives

1+2\sin x\cos x=\frac{1}{25},

\sin x\cos x=-\frac{12}{25}.

Thus

\sin x

and

\cos x

are the roots of

t^2-\frac15t-\frac{12}{25}=0,

namely

\frac{4}{5}

and

-\frac{3}{5}.

Because

\sin x\ge0

on the given interval,

\sin x=\frac{4}{5}

and

\cos x=-\frac{3}{5}.

Hence

\tan x=-\frac{4}{3}.

Therefore, the correct answer is A.