Proving Trigonometric Identity: cosx/1-sinx + 1-sinx/cosx = 2secx + 2tanx

[brianlane24]

cosx/1-sinx + 1-sinx/cosx = 2secx + 2tanx
I can get to 2secx + tanx - tanx, any help is appreciated

 

[rock.freak667]

Type out all the working you have done, if you do not do that, then we won't know where you've reached and how to help you go towards the end result of the proof.

 

[brianlane24]

(cosx)/(1-sinx) x (1+sinx)/(1+sinx) + (1-sinx)/(cosx) x (cosx)/(cosx)
(cosx+sinxcosx)/(1-sin^2x) + (cosx-sinxcosx)/cos^2x
(cosx/cos^2x)+(sinxcosx/cos^2x) + cosx/cos^2x - (sinxcosx/cos^2x)
1/cosx + sinx/cosx + 1/cosx - sinx/cosx
2secx

 

[rock.freak667]

I've tried both sides and can only get 2secx on the LHS and 2cosx/(1-sinx) on the RHS...the problem is written down correctly right?

 

[brianlane24]

I'm fairly certain, that is what the worksheet said,

 

[brianlane24]

When I worked from the RHS, i got to
(2cosx/1-sin^2x) + (2sinxcosx/1-sin^2x)

 

[brianlane24]

Nevermind, thank you, my teacher wrote down the wrong question

 

[Mark44]

It's no wonder you can't prove it: The equation you gave is not an identity. I tried it with a specific value of x, pi/4, for which sin(pi/4) = sqrt(2)/2 = cos(pi/4), and tan(pi/4) = 1.

The value on the left side was 2sqrt(2), and on the right it was 2sqrt(2) + 2.

Are you sure that:

1. you copied the equation correctly?
2. you weren't supposed to solve the equation rather than prove it was an identity?