Question 1064981
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As you know (or must to know)

sin(2x) = 2*sin(x)*cos(x).


Now trace my steps:


if  sinx + cosx = 4/3  then  {{{(sin(x) + cos(x))^2}}} = {{{16/9}}},   or

{{{sin^2(x) + 2*sin(x)*cos(x) + cos^2(x)}}} = {{{16/9}}},

1 + 2*sin(x)*cos(x) = {{{16/9}}},

2*sin(x)*cos(x) = {{{16/9-1}}} = {{{-2/9}}},

Therefore,

sin(2x) = {{{-2/9}}}.
</pre>

Solved.