Prove trig identities Help !!

mike--1988 · #1 $Old$ November 21st, 2009, 05:24 AM

hi everyone, im new

ive been stuck on these two questions for a while and was wondereing if anyone can help,
these are the proof identity questions..

1) secx / tanx + cotx = sinx

2) (cosx / sinx + 1) + (sinx + 1 / cosx) = 2secx

thanks..

skeeter · #2 $Old$ November 21st, 2009, 05:46 AM

Quote:

Originally Posted by mike--1988 $View Post$

hi everyone, im new

ive been stuck on these two questions for a while and was wondereing if anyone can help,
these are the proof identity questions..

1) secx / tanx + cotx = sinx

2) (cosx / sinx + 1) + (sinx + 1 / cosx) = 2secx

thanks..

$\frac{\sec{x}}{\tan{x}+\cot{x}} \cdot \frac{\tan{x}}{\tan{x}} =$

$\frac{\sec{x}\tan{x}}{\tan^2{x}+1} =$

$\frac{\sec{x}\tan{x}}{\sec^2{x}} =$

$\frac{\tan{x}}{\sec{x}} =$

$\frac{\sin{x}}{\cos{x}} \cdot \frac{\cos{x}}{1} = \sin{x}$

mosta86 · #3 $Old$ November 21st, 2009, 06:29 AM

(cosx / sinx+1 ) + (sinx + 1 / cos x )
1. make common doniminator , then u will get :
( (cosx)^2 + ( sinx + 1 )^2 ) / (( sinx + 1 )cosx ) =

( (cosx)^2 + (sinx)^2 + 2 sinx + 1 ) / (( sinx + 1 )cosx ) =

( 2 + 2 sinx ) / (( sinx + 1 )cosx ) =
2 ( 1 + sinx ) / (( sinx + 1 )cosx ) =
2/cosx = 2 secx.