Question

Given $\sin x+\cos x=\frac{5}{4}$. If $1+2\sin x\cos x=a,$ then $32a=$

• A. 10
• B. 32
• C. 50
• D. 1

Answer 1

The correct option is C 50

Given, $\sin x+\cos x=\frac{5}{4}$

Squaring both the sides, we get,
$(\sin x+\cos x{)}^2=\frac{25}{16}$
$\Rightarrow {\sin }^{2}x+{\cos }^{2}x+2\sin x\cos x=\frac{25}{16}$
$\Rightarrow 1+2\sin x\cos x=\frac{25}{16}$
But, $1+2\sin x\cos x=a$
$\Rightarrow a=\frac{25}{16}$
$\Rightarrow 32a=\frac{25}{16}\times 32=50$