Question

if y = 2/sin theta + root 3 cos theta then the minimum value of y is

Answer 1

Heya Mate!!!

$\blue{\huge{\underline{\star\: Solution\: \star}}}$

Y =2/(sinθ + √3cosθ)

So, -√(1 + √3²) ≤ (sinθ + √3cosθ) ≤ √(1 + √3²)

-2 ≤ (sinθ + √3cosθ) ≤ 2

So, minimum value of (sinθ + √3cosθ) = -2

Maximum value of (sinθ + √3cosθ) = 2

For getting minimum value of y , we have to use maximum value of (sinθ + √3cosθ) .

So, minimum value of y = 2/-2 = 1

$\red{\huge{\underline{\star\:Answer=1\: \star}}}$

Answer 2

Y =
$\frac{2}{ \sin(x) + \sqrt{3} \cos(x) }$
K = minimum if Sinx + √3cosx is maximum

K will be maximum when Cosx = √3/2 that is Cos30°
K = sin30° + √3cos30°
K = 1/2 + √3/2
K = 4/2
k = 2

Then Y = 2/2
Y = 1

Minimum value will be 1