Question

Solve the equation `sintheta+costheta=sqrt2cosalpha`?

Answer 1

`theta=2npi+pi/4+-alpha`

Explanation:

`sintheta+costheta`

= `sqrt2(costhetaxx1/sqrt2+sinthetaxx1/sqrt2)`

= `sqrt2(costhetacos(pi/4)+sinthetasin(pi/4))`

= `sqrt2cos(theta-pi/4)`

Hence `sintheta+costheta=sqrt2cosalpha`

is equivalent to `sqrt2cos(theta-pi/4)=sqrt2cosalpha`

or `cos(theta-pi/4)=cosalpha`

i.e. `theta-pi/4=2npi+-alpha`

or `theta=2npi+pi/4+-alpha`