यदि $a cot\theta +b cosec \theta =x^2$ and $ b cot \theta + a cosec \theta =y^2$, तो $(x^4 - y^4)$ का मान ज्ञात करें?
Solution
$x^4 - y^4 \Rightarrow (x^2)^2 - (y^2)^2$
$\Rightarrow a^2 \cot^2 \theta + 2ab~ \cot \theta~ cosec~ \theta + b^2~ cosec^2 \theta - b^2 \cot^2 \theta + 2ab \cot \theta ~cosec \theta -a^2 cosec^2~ \theta $
$\Rightarrow b^2 (cosec^2~ \theta - \cot^2 \theta)-a^2 (cosec^2~ \theta - \cot^2 \theta)$
$= b^2 -a^2 [\because ~cosec^2~ \theta -\cot^2 \theta = 1]$