Question

√3 cosФ + sinФ=√2 solve this equation

Answer 1

using rules of sin(a+b) formula
sin(a+b) = sin(a)*cos(b) + sin( b)*cos(a) ...(1)
so taking 2 as common in question equation
=> 2( √3/2 cos¢ + 1/2 sin¢) = √2
=> 2( sin60° * cos¢ + cos60° * sin¢) = √2
comparing last equation with equation one we get
=> 2( sin( ¢ + 60° ) ) = √2
=> sin( ¢ +60° ) = 1/√2

and we know that sin (nπ + π/4) = 1/√2 (where n is any integer)
so now
=> ¢ + π/3 = nπ + π/4
=> ¢ = nπ - π/12 ( where n can be any integer)