Question

8cosec^2a +25sin^2a=?

Answer 1

Given:

$P(a)=8cosec^2a +25sin^2a$

To Find:

$8cosec^2a +25sin^2a=?$

Solution:

             $P(a)=8cosec^2a +25sin^2a\\ =8(1/sin^{2}a )+25sin^{2}a\\ =(8+25Sin^{4}a )/sin^{2} a\\ =(8+25sin^{2}a )cosec^{2}a$

since, $sin^{2} a={1}/{cosec^{2}a }$ and vice-versa.

Hence,

        $8cosec^2a +25sin^2a=(8+25sin^{4}a)cosec^{2}a$