ત્રિકોણમિતિય વિધયો — ગણિત ધોરણ 11 સાયન્સ — Question

$\therefore a^2 sec^2 \alpha - b^2 tan^2 \alpha = c^2$

$\therefore a^2 \left(1 + tan^2 \alpha\right) - b^2 tan^2 \alpha = c^2$

$\therefore a^2 + a^2 tan^2 \alpha - b^2 tan^2 \alpha = c^2 $

$\therefore \left(a^2 - b^2\right) tan^2 \alpha = c^2 - a^2$

$\therefore tan^2 \alpha =\frac{c^2-b^2}{ a^2 -b^2}$

$\therefore 1 + cot^2 \alpha = \frac{1+a^2-b^2}{c^2-a^2}$

$\therefore cosec^2 \alpha = \frac{c^2 -a^2 + a^2 - b^2}{c^2 - a^2}$

$\therefore sin^2 \alpha = \frac{c^2 - a^2}{c^2 - b^2}$