Question

Find the maximum value of 3 sin A + 4 cos A + 12
A) 7
B) 17
C) 15
D) 25
Quality answer required .​

Answer 1

Answer:

OPTION B  does not seem correct but It is CORRECT !

Explanation:

Maximum value of 3 sin A + 4 cos A + 12 depends on the variable sin A . But directly , it does not depend on 12 .

Hence the value of the equation 3 sin A + 4 cos A + 12 is maximum when the value of 3 sin A + 4 cos A is maximum .

Now we are required to find the value which is maximum for 3 sin A + 4 cos A .

Someone will advise you to differentiate the equation which is lengthy and time taking . I will say you to apply a simpler formula which is helpful in competitive exams .

So better start with the problem than waste time talking :-

Maximum value of a cos A + b sin A is given by this formula :

+ √( a² + b² )

When you are asked for minimum just change the (+) to (-) :

- √( a² - b² )

So the maximum value of 3 sin A + 4 cos A is as follows :

√( 3² + 4² )

⇒ √( 9 + 16 )

⇒ √25

⇒ 5

This means that whatever be the value of A , 3 sin A + 4 cos A cannot be more than 5 .

3 sin A + 4 cos A + 5 will have the maximum value of :

Maximum value of 3 sin A + 4 cos A + 5

⇒ 12 + 5

⇒  17

17 is the answer to the question .

Answer 2

HEYA MATE ❤ ❤

Find the maximum value of 3 sin A + 4 cos A + 12

A) 7

B) 17 ✅✅

C) 15

D) 25