Question

প্রমাণ কর যে, $\frac{1}{1+sin^2\theta}+\frac{1}{1+cosec^2\theta}=1$

Answer 1

Left Hand Side
$=\frac{1}{1+sin^2\theta}+\frac{1}{1+cosec^2\theta}$

$=\frac{1}{1+sin^2\theta}+\frac{1}{1+\frac{1}{sin^2\theta}}$

$=\frac{1}{1+sin^2\theta}+\frac{1}{\frac{sin^2\theta+1}{sin^2\theta}}$

$=\frac{1}{1+sin^2\theta}+\left(1 \times \frac{sin^2\theta}{sin^2\theta+1}\right)$

$=\frac{1}{1+sin^2\theta}+\frac{sin^2\theta}{1+sin^2\theta}$

$=\frac{1+sin^2\theta}{1+sin^2\theta}$

$=1$

$=$ Right Hand Side

[Proved]