Question

given sinx+cosx=5/4. If 1+2sinxcosx=a,then find the value of 32a.

Answer 1

$\sin(x) + \cos(x) = \frac{5}{4} \\ squaring \: \: both \: \: sides\\ {( \sin(x) + \cos(x) )}^{2} = \frac{25}{16} \\ { \sin}^{2} (x) + { \cos}^{2} (x )+ 2 \sin(x) \cos(x) = \frac{25}{16} \\ 1+ 2 \sin(x) \cos(x) = \frac{25}{16} \\ \\ therefore \\ a = \frac{25}{16} \\ 32a = 32 \times \frac{25}{16} = 50$