Question
Fri September 28, 2012 By:

not able open the ans.

Expert Reply
Fri September 28, 2012

4 cosec2 A + 9 sin2 A = 4/ sin2 A + 9 sin2 A = (4 + 9 sin4 A)/ sin2 A

Let F(A) = (4 + 9 sin4 A)/ sin2 A

(A) = [(4 × 9 sin3 A. cos A) (sin2 A) - (4 + 9 sin4 A) × 2 cos A. sin A] / (sin2 A)2

 

This on further simplification gives

(A) =  2cos A. (9 sin4 A - 4)/ sin3 A

 

To find the maximum or the minimum value, it is required to consider, 2cos A. (9 sin4 A - 4)/ sin3 A = 0

This gives cos A = 0 or sin2 A = 2/3.

 

The maximum value of cosec2 A is infinite. In that case sin2 A = 0.

So, maximum value of F(A) is infinite.

 

When cos A = 0 i.e. sin2 A = 1, then F(A) = 4 × 1 + 9 × 1 = 13

When sin2 A = 2/3, i.e. cosec2 A = 3/2, then F(A) = 4 × 3/2 + 9 × 2/3 = 12.

Among 12 and 13, the minimum value is 12.

So, the minimum value of F(A) is 12.

Related Questions
Fri January 06, 2017

Tue November 29, 2016

Q)

Ask the Expert