Question

if sin A + cos A =√3 then the value of sin A cos A is​

Answer 1

Answer:

The answer is 1

Step-by-step explanation:

Given  $\sin A+\cos A=\sqrt 3$

Square both sides

          $(\sin A+\cos A)^2=(\sqrt 3)^2$

         $\Rightarrow \sin^2A+\cos^2A+2\sin A\cos A=3$

         $\Rightarrow 1+2\sin A\cos A=3$

         $\Rightarrow 2\sin A\cos A=3-1=2$

         $\Rightarrow \sin A\cos A=\frac{2}2=1$

(Theoretically $\sin A+\cos A$ cannot be $\sqrt 3$)