Question

If Sin A + Cos A = 1.4 , then Sin A . Cos A = ______________.​

Answer 1

Correct Answer is 0.48.

Kindly see the attachment for explanation .

Answer 2

$\qquad \quad \large {\pmb{ \frak {\overline{ \underline {\bigstar{ \purple{required \: solution} \bigstar }}}}}}$

$\large \frak{given} \begin{cases} \large \sf{ \sin A + \cos A = \frak{1.4}} \end{cases}$

❍ Squaring Both the sides ...

________________________

$: \implies \sf (\sin A + \cos A) ^{2} = {1.4}^{2}$

$:\implies \sf { \sin}^{2} A + { \cos}^{2} A+ 2 \sin A\cos A= 1.96$

As we know that :-

❍ $\dag \underline{ \boxed {\pink{{ \frak{ \sin ^{2} \theta + \cos ^{2} \theta = 1 }}}}}$

$\: \: \: \: \: \: : \implies \sf 1 + 2 \sin A\cos A = 1.96$

$\: \: \: \: \: \: : \implies \sf \: 2 \sin A \cos A= 0.96$

$\: \: \: \: \: \: : \implies \sf \sin A\cos A= \cancel \dfrac{0.96}{2}$

$\: \: \: \: \: \: : \implies \: \boxed {\pink{{ \frak{\sin A\cos A= 0.48}}}} \bigstar$

I hope it's beneficial :D