Question

The maximum value of 3 cos + 4 sinis
(a) 3
(b) 4
(d) None of these
(c) 5​

Answer 1

Answer:

d

none of these

because it doesn't have value

Answer 2

Answer:

5

Step-by-step explanation:

let x be the angle of sin and cos

Let us assume y = 3sin x + 4cos x

Now for maximum value, dy/dx = 0

=> d/dx (3sinx + 4cosx) = 0

y' = 3cosx - 4sinx = 0

Now, on checking, we find that dy'/dx < 0

=> 3cosx = 4sinx gives the value of x which will give the maximum value of y

Tanx= 3/4

X = tan^-1(3/4)

= 37 degree

Therefore, maximum value of y = 3 sin37° + 4 cos 37°

3(3/5) + 4(4/5)

=25/5 = 5

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