Posted by **Shubham** on Thursday, May 22, 2008 at 9:33am.

sin(x)+cos(x)=2/3

find the value of

sin(x)

- Maths -
**Reiny**, Thursday, May 22, 2008 at 10:25am
square both sides

sin^2 x + 2sinxcosx + cos^2 x = 4/9

1 + sin 2x = 4/9

sin 2x = -5/9

2x = 213.75 or 2x = 326.25

x = 106.87º or x = 163.126º

but since we performed a "squaring" operation we have to verify each answer.

when x = 106.87 , sin106.87 + cos106.87 = .66676.., so that works

but for x= 163.126, the result was -.66676 which is NOT the right side

so sinx = sin106.87 = .9569

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