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Question: Answered & Verified by Expert
 The minimum value of 2sinx+2cosx is :
MathematicsFunctionsJEE MainJEE Main 2020 (04 Sep Shift 2)
Options:
  • A 2-1+12
  • B 2-1+2
  • C 21-2
  • D 21-12
Solution:
2747 Upvotes Verified Answer
The correct answer is: 21-12

Using A.M≥G.M.

2sinx+2cosx2≥2sinx·2cosx

⇒2sinx+2cosx≥21+sinx+cosx2

Now    -2≤sinx+cosx≤2

So minimum value of 

2sinx+2cosx=21+-22=21-12  

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