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Question
The minimum value of 3cosx + 4sinx + 8 is ______.
Options
5
9
7
3
Solution
The minimum value of 3cosx + 4sinx + 8 is 3.
Explanation:
The given expression is 3cosx + 4sinx + 8
Let y = 3cosx + 4sinx + 8
⇒ y – 8 = 3cosx + 4sinx
Minimum value of y – 8 = `sqrt((3)^2 + (4)^2`
⇒ y – 8 = `-sqrt(9 + 16)` = – 5
⇒ y = 8 – 5 = 3
So, the minimum value of the given expression is 3.
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