Question

Y=2/(sin theta + √3 cos theta), then the minimum value of y is?

Answer 1

Answer:

see the attachment.....

Step-by-step explanation:

Answer 2

minimum value of y is when denominator is maximum.

let theta be alpha

consider denominator

• $\sin( \alpha ) + \sqrt{3} \cos( \alpha )$
• divide whole by(1^2+root3^2)=2

• $\sin( \alpha ) \frac{1}{2} + \\ \ \cos( \alpha ) \frac{ \sqrt{3} }{2}$
• it is of form sin a cos b + cos a sin b = sin(a+b)

now ,

equation becomes

$\sin( \alpha + 60)$

now sin is maximum at theta =90

this means

sin alpha+60 must be equal to sin 90

alpha =30 degree

this means theta =30

put theta = 30 in given q

so y= 2/(1/2+root3×root3/2)

y=1