Question

if y = sine @ + root3 cos@, then the maximum value of
y is
(1) 1
(2) 4
(3) 2
(4) 3​

Answer 1

Answer:

Maximum value of y = 2

Explanation:

I think you want to ask that

$y = sin \: \theta + \sqrt{3} \:cos \: \theta$

than find the maximum value of y

To solve this,multiply and divide eq by 2

$y =2( \frac{1}{2} sin \: \theta + \frac{ \sqrt{3} }{2} cos \: \theta) \\ \\ y = 2(cos \: 60° \: sin \: \theta + sin \: 60° \: cos \: \theta) \\ \\ y = 2 \: sin(60° + \theta)$

Now to find the maximum value of y,differentiate both side by theta

$\frac{dy}{d \theta} = 2cos(60° + \theta) \\ \\ 2cos(60° + \theta) = 0 \\ \\ cos(60° + \theta) =0 \\ \\ 60° + \theta = {cos}^{ - 1} (0) \\ \\ 60° + \theta = 90° \\ \\ \theta = 30°$

Maxima present on 30°,put the value of theta,to find the maximum value

$y = sin \: 30° + \sqrt{3} cos \: 30° \\ \\ = \frac{1}{2} + \sqrt{3} \times \frac{ \sqrt{3} }{2} \\ \\ = \frac{1}{2} + \frac{3}{2} \\ \\ = \frac{4}{2} \\ \\ y= 2$

Option 3 is correct.

Hope it helps you.

Answer 2

Answer:

maximum value of Y is = 2