[tex]sin\alpha + cos\alpha = \frac34\\\\sin^2\alpha+cos^2\alpha=1\\\\(sin\alpha+cos\alpha)^2=sin^2\alpha+cos^2\alpha+2sin\alpha cos\alpha\\\\1+2sin\alpha cos\alpha=(\frac34)^2\\2sin\alpha cos\alpha=\frac9{16}-1\\2sin\alpha cos\alpha=-\frac7{16}[/tex]
