Question

Find the minimum value of 5cosA + 12sinA + 12 .

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Answer 1

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Answer 2

ANSWER

Given=

>5cosA + 12sinA + 12

=>13{$\dfrac{5}{13}CosA$ + $\dfrac{12}{13}SinA$} + 12

Let, Cos $\theta=\dfrac{5}{13}$

then Sin$\theta=\dfrac{12}{13}$

So we get =>

=>13(CosA × $Cos\theta + SinA \times Sin\theta$) +12

=>13{Cos$(A - \theta)$}

Here the minimum value of {Cos$(A -\theta )$} is -1.

Hence the minimum value of 5cosA + 12sinA + 12 will be -13 + 12=-1.