Question

if sin theta +cos theta=root2 then find the value of sin theta×cos theta

Answer 1

Hey there !

Solution:

Given that,

Sin A + Cos A = √2

To find: Sin A . Cos A = ?

Proof:

Sin A + Cos A = √2

Squaring on both sides we get,

=> ( Sin A + Cos A )² = ( √2 )²

=> Sin²A + Cos²A + 2 SinA.CosA = 2

=> 1 + 2 SinA.CosA = 2

=> 2 SinA.CosA = 2 - 1 = 1

=> SinA.CosA = 1 / 2

Hence the answer is 1 / 2 .

Hope my answer helped !