Question

The minimum value of 3 cos A + 4 sin A + 5 is :

(A) 5 (B) 9 (C) 7 (D) 3​

Answer 1

Answer:

Option A (5) is the correct answer

Step-by-step explanation:

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Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

The minimum value of 3 cos A + 4 sin A + 8 is

(A) 5

(B) 9

(C) 7

(D) 3

FORMULA TO BE IMPLEMENTED

For a cos A + b sin A

$\sf{Maximum \: value = \sqrt{ {a}^{2} + {b}^{2} } }$

$\sf{ Minimum \: value = - \sqrt{ {a}^{2} + {b}^{2} } }$

EVALUATION

Here the given expression is 3 cos A + 4 sin A + 5

Now minimum value of 3 cos A + 4 sin A

$= - \sqrt{ {3}^{2} + {4}^{2} }$

$= - \sqrt{9 + 16}$

$= - \sqrt{25}$

$= - 5$

Hence the required minimum value of

3 cos A + 4 sin A + 8 is

= - 5 + 8

= 3

FINAL ANSWER

Hence the correct option is (D) 3

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