Question

Fint the value of `Sin theta + Cos theta` ?

If `Sin theta * Cos theta=1/2` find the value of `Sin theta + Cos theta`

Answer 1

`sqrt2`

Explanation:

`sinthetaxxcostheta=1/2`

`=>2sinthetacostheta=1`

`=>sin2theta=sin90^o`
`=>2theta=90^o`
`:.theta=45^o`
`sintheta+costheta=sin45^(o)+cos45^o=1/sqrt2+1/sqrt2=2/sqrt2=sqrt2(Ans.)`

Answer 2

Another approach...

Explanation:

Given:-

`sintheta cdot costheta=1/2`

`=>2 cdot sintheta cdot costheta=1`

`"So,"`

`sintheta +costheta`

`=sqrt((sintheta+costheta)^2)`

`=sqrt(sin^2theta+2 cdot sintheta cdot costheta+cos^2theta`

`=sqrt((sin^2theta+cos^2theta)+2 cdot sintheta cdot costheta`

`=sqrt(1+1)`

`=sqrt2`

Hope it helps...

Thank you...

:-)