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Question

If y = 2/(sin theta + √3 cos theta), then find the minimum value of y


Solution

Y =2/(sinθ + √3cosθ)
for solving this question, you should understand one thing 
- ≤ asinx + bcosx ≤

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 

Hence, =1

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