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

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

Grade:12

2 Answers

Arun
25763 Points
3 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.
In case of any difficulty, please feel free to ask.
Soumendu Majumdar
159 Points
3 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!

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