Question

sin theta +cos theta =root 3,find the Vale of sin theta ×cos theta

Answer 1

According to given sum,

I will take theta as alpha.

$\sin( \alpha ) + \cos( \alpha ) = \sqrt{3}$

squaring on both sides

${( \sin( \alpha ) + \cos( \alpha ) )}^{2} = { \sqrt{ 3} }^{2}$

${ \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} + 2 \sin( \alpha ) \cos( \alpha ) = 3$

$1 + 2 \sin( \alpha ) \cos( \alpha ) = 3$

$2 \sin( \alpha ) \cos( \alpha ) = 3 - 1 = 2$

$\sin( \alpha ) \cos( \alpha ) = \frac{2}{2} = 1$

:Hope it helps u.