SOLUTION: if sinx + cosx = 4/3 then sin2x = ?

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Question 1064981: if sinx + cosx = 4/3 then sin2x = ?
Answer by ikleyn(52814) About Me  (Show Source):
You can put this solution on YOUR website!
.
As you know (or must to know)

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


Now trace my steps:


if  sinx + cosx = 4/3  then  %28sin%28x%29+%2B+cos%28x%29%29%5E2 = 16%2F9,   or

sin%5E2%28x%29+%2B+2%2Asin%28x%29%2Acos%28x%29+%2B+cos%5E2%28x%29 = 16%2F9,

1 + 2*sin(x)*cos(x) = 16%2F9,

2*sin(x)*cos(x) = 16%2F9-1 = -2%2F9,

Therefore,

sin(2x) = -2%2F9.

Solved.