Question

the least value of 4 cosec^2 A + 9 sin^2 A is: ?
a)10
b)11
c)12
d)14

Answer 1

I have got an answer by differentiating with respect to A and putting the result equal to zero. Then solving for A and substituting the value for A in the original expression.

Answer 2

\[y=4\csc ^{2}A+9\sin ^{2}A\]
\[\frac{dy}{dA}=(-8\csc ^{2}A \times \cot A)+18\sin A \cos A=0\]

Answer 3

@dhiwagm
use this hint
\[4 \csc^2 A+9 \sin^2 A=\frac{4}{\sin^2 A}+9 \sin^2 A=\frac{4}{\sin^2 A}+9 \sin^2 A-12+12 \\ =(\frac{2}{\sin A}-3 \sin A)^2+12\]
answer is 12