Question

If
Theta is acute then
Prove that
sin theta+ cos theta›1​

Answer 1

we should know that

sin²x+cos²x=1

let

sinx+cosx=k

then

(sinx+cosx)²=k²

sin²x+cos²2sinx*cosx=k²

1+2sinx*cosx=k²

since x is acute this means x lies in 1st quadrant

In 1st quadrant sinx and cosx are positive

therefore

2sinx*cosx=positive

we also know that

√(1+a)>1

where a=some positive constant

Hence

1+2sinx*cosx=k²

k=√(1 + positive value)

>1

k>1

sinx + cosx > 1

Hope this helps.