split - Trig Identity

[ladyluck4772]

Verify cos x/(1-sinx) = secx - tanx

I am working the same problem and have come up with the following. However, I am unsure of where to go now. Can someone please help?

secx (1-sinx) = secx - tanx

secx (1 - (cosx) (tanx)) = secx - tanx

secx (1-(1/secx) (tanx)) = secx - tanx

 

[Deleted member 4993]

Verify cos x/(1-sinx) = secx - tanx

I am working the same problem and have come up with the following. However, I am unsure of where to go now. Can someone please help?

secx (1-sinx) = secx - tanx

secx (1 - (cosx) (tanx)) = secx - tanx

secx (1-(1/secx) (tanx)) = secx - tanx

Please start a new thread with new problem.

work from one-side of the equation only.

sec(x) * [1-sin(x)]

= 1/cos(x) * [1-sin(x)] ........ multiply and distribute

= 1/cos(x) - 1/cos(x) * sin(x)

= 1/cos(x) - sin(x)/cos(x)

and continue...

 

[ladyluck4772]

Still need help. Thank you!

Verify cosx/(1+sinx) = secx -tanx

OK, I got to where you stopped and continued to:

1/cosx - tanx =

[1/(1/secx)] - tanx =

(1-tanx)/secx * secx/secx =

(1-tanx)/secx =

And I am stuck again. Please help.

Lori


P.S. I didn't know if I was supposed to make a new thread for this reply. Sorry if I was.

 

[Deleted member 4993]

Verify cosx/(1+sinx) = secx -tanx

OK, I got to where you stopped and continued to:

1/cosx - tanx = sec(x) - tan(x) .........................................Done


And I am stuck again. Please help.

Lori


P.S. I didn't know if I was supposed to make a new thread for this reply. Sorry if I was.

.

 

[guitarguy]

It might be easier to manipulate the right side of the equation and see if it is equal to the left side.

Substitutions you might try: secx = 1/cosx and tanx = sinx/cosx

Keep up your good efforts