Question

if sin teta + cos teta =square root of 2 then
sin teta × cos teta

Answer 1

Sin + cos = root2
Squaring both sides we get,
( Sin + cos) ² = 2
Sin² + cos² + 2 sin cos = 2
1 + 2 sin cos = 2
2 sin cos = 1
Sin cos = 1/2

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Answer 2

let theta be a to make the anser simple

sin a+cos a=√2

squaring both sides

sin^2a +cos^2a+2 sina cosa=2

1+ 2 sina cosa = 2

2 sina cosa =1

sina cosa =1/2