i need help proving the indentity

• Nov 5th 2009, 03:31 PM
valvan
i need help proving the indentity
(1/1-sinx)-(1/1+sinx)=2sectan
i got stumped on this one
• Nov 5th 2009, 03:42 PM
alexmahone
Quote:

Originally Posted by valvan
(1/1-sinx)-(1/1+sinx)=2sectan
i got stumped on this one

$\frac{1}{1-sinx}-\frac{1}{1+sinx}$

= $\frac{2sinx}{1-sin^2x}$

= $\frac{2sinx}{cos^2x}$

= $2\frac{1}{cosx}\frac{sinx}{cosx}$

= $2secxtanx$
• Nov 5th 2009, 03:52 PM
valvan
can you explain further how you got to
= http://www.mathhelpforum.com/math-he...99e50587-1.gif
• Nov 5th 2009, 05:59 PM
Quote:

Originally Posted by valvan
can you explain further how you got to
= http://www.mathhelpforum.com/math-he...99e50587-1.gif

HI

$\frac{1}{1-sinx}-\frac{1}{1+sinx}$

Just combine the fractions .

$\frac{1+\sin x}{(1-\sin x)(1+\sin x)}-\frac{1-\sin x}{(1+\sin x)(1-\sin x)}$
• Nov 5th 2009, 08:49 PM
pacman
http://www.mathhelpforum.com/math-he...393dc78c-1.gif = Numerator/Denomenator

Numerator = (1 + sin x) - (1 - sin x) = 1 + sin x - 1 + sin x = ?