Question

If $si{n}^2\theta +co{s}^2\theta =1=\lambda si{n}^2\theta co{s}^2\theta ,$ find the value of $\lambda$.

Answer 1

$\Rightarrow \sin {}^2\theta +\cos {}^2\theta =\lambda \sin {}^2\theta \cos {}^2\theta \Rightarrow \lambda =\frac{1}{\sin {}^2\theta \cos {}^2\theta }\Rightarrow \lambda =4\csc {}^{2}2\theta$