Posted by **Matt** on Tuesday, January 31, 2012 at 1:38pm.

Prove (1+secx)/(tanx+sinx)=cscx

- trig -
**MathGuru**, Tuesday, January 31, 2012 at 8:07pm
Let's use a few identities:

secx = 1/cosx

tanx = sinx/cosx

cscx = 1/sinx

Therefore:

(1 + 1/cosx)

------------ = cscx

(sinx/cosx + sinx)

Change 1 in the numerator to cosx/cosx, which is the equivalent of 1. Also, multiply sinx in the denominator by cosx/cosx.

(cosx/cosx + 1/cosx)

-------------------- = cscx

(sinx/cosx + sinx(cosx)/cosx)

(cosx + 1)/cosx

---------------- = cscx

[sinx + sinx(cosx)]/cosx

(cosx + 1)/[sinx + sinx(cosx)] = cscx

(cosx + 1)/sinx(cosx + 1) = cscx

1/sinx = cscx

cscx = cscx

I hope this helps.

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