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December 21, 2014

December 21, 2014

Posted by **Alycia** on Thursday, November 1, 2012 at 10:37pm.

Problem 1. Sinx/(cotx+1) + cosx/(tanx+1) = 1/(sinx+cosx)

Problem 2. sinx + cosx + sinx + tanx + cosxcotx = secx + cscx

Problem 3. ((sinx + cosx)/(1 + tanx))^2 + ((sinx - cos^2x)/(1 - cotx))^2 = 1

Problem 4. ((1 + sinx)/cosx) + (cosx/(1 + sinx)) = 2secx

- Math -
**Steve**, Friday, November 2, 2012 at 1:50amoften it's easier to work with just sin and cos.

working just on the left side, we have

sin/(cot+1) + cos/(tan+1)

sin/(cos/sin+1) + cos/(sin/cos+1)

sin^2/(cos+sin) + cos^2(sin+cos)

(sin^2 + cos^1)/(sin+cos)

1/(sin+cos)

ta-daaaah

- Math -
**Reiny**, Friday, November 2, 2012 at 7:46am2. I think you have a typo , it should have been

sinx + cosx + sinxtanx + cosxcotx = secx + cscx

LS = sinx + cosx + sinx(sinx/cosx) + cosx(cosx/sinx

using a LCD of sinxcosx

= (sin^2x cosx + sinxcos^2x) + sin^3 x + cos^3 x)/(sinxcos)

= (cosx(sin^2 x + cos^2 x) + sinx(sin^2 x + cos^2 x) )/(sinxcosx)

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

= cosx/(sinxcosx) + sinx/(sinxcosx)

= 1/sinx + 1/cosx

= cscx + secx

= RS

try the others, following Steve's suggestion of changing all into sines and cosines

- Math -
**Alycia**, Friday, November 2, 2012 at 8:13amthank you so much

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