# √3 cosA + SinA =√2 solve the trigonometric equation

Arun
25763 Points
4 years ago
Dear Deepak

Divide by 2
Sqrt(3)/2 cos A + ½ sinA = 1/sqrt(2)
Cos (A- pi/6) = cos (pi/4)
Now use
costheta = cos x
Now you van solve on you own.
Soumendu Majumdar
159 Points
4 years ago
Dear Student,
To make the problem easier first divide both L.H.S & R.H.S by 2
so ($\sqrt{3}/2$) cos A + (1/2)sin A =
Now cos $30^{\circ}$ = $\sqrt{3}/2$ and sin $30^{\circ}$ = ½ and cos $45^{\circ}$ = $1/\sqrt{2}$
so cos  $30^{\circ}$cos A + sin  $30^{\circ}$sin A = cos $45^{\circ}$
Using the formula cos X cos Y + sin X sin Y = cos(X – Y)
so cos( A – $30^{\circ}$) = cos $45^{\circ}$
so A – $30^{\circ}$ = $45^{\circ}$
implies A = $75^{\circ}$ (ANS)

Hope it helps!