Question

10 POINTS.

PROVE THAT :-
$\frac{sec - tan }{sec + tan} = 1 - 2sec.tan + {tan}^{2}$

Answer 1

we know, (sec²x - tan²x) = 1

(secø - tanø)/(sec ø + tanø) = 1 - 2secø.tanø + 2tan²ø
taking ø = x

(secx - tanx)/(secx + tanx) * (secx - tanx)/(secx - tanx)

(secx - tanx)²/(sec²x - tan²x)

sec²x + tan²x - 2secx.tanx

(1 + tan²x) + tan²x - 2secx.tanx

1 + 2tan²x - 2secx.tanx.