Question

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⚡Answer the question.⚡

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

Answer 1

Answer :

Minimum value of 5 cos A + 12 sin A = - √( 5² + 12² )

⇒ -√( 25 + 144 )

⇒ - √( 169 )

⇒ - 13

Hence 5 cos A + 12 sin A will have the minimum value of - 13 .

The minimum value of 5 cos A + 12 sin A + 12 will be :

- 13 + 12

⇒ - 1

The minimum value of the equation is - 1 .

Explanation :

The minimum value of a cos A + b sin A = - √( a² + b² )

The maximum value of a cos A + b sin A = + √( a² + b² )

Hence we will find the minimum value of 5 cos A + 12 sin A by putting 'a' as 5 and 'b' as 12 .

Then after getting the value add 12 to the minimum value and we will get our answer .

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 × 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.