ত্রিকোমিতি ৯.১ এর ৭(গ) সমাধান।
7) গ) $\displaystyle \frac{1}{1+sin^{2} A} +\frac{1}{1+cosec^{2} A} =1$
L.H.S= $\displaystyle \frac{1}{1+sin^{2} A} +\frac{1}{1+cosec^{2} A}$
$\displaystyle =\frac{1}{1+sin^{2} A} +\frac{1}{1+\frac{1}{sin^{2} A}}$
$\displaystyle =\frac{1}{1+sin^{2} A} +\frac{1}{\frac{sin^{2} A+1}{sin^{2} A}}$
$\displaystyle =\frac{1}{1+sin^{2} A} +\frac{sin^{2} A}{1+sin^{2} A}$
$\displaystyle =\frac{1+sin^{2} A}{1+sin^{2} A}$
$\displaystyle =1$
=R.H.S ( Proved).
