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December 22, 2014

December 22, 2014

Posted by **Heather** on Friday, August 15, 2014 at 12:14pm.

1. cosx + 1/sin^3x = cscx/1 - cosx

I changed the 1: cosx/sin^3x + sin^3x/sin^3x = cscx/1-cosx

Simplified: cosx + sin^3x/sin^3x = cscx/1-cosx

I don't know where to go from there.

2. (sinx + cosx)(tanx + cotx) = secx + cscx

I made this into (sinx + cosx)(sinx/cosx + cosx/sinx) = secx + cscx

FOILed: sin^2x/cosx + sinxcosx/sinx + sinxcosx/cosx + cos^2x/sinx

Did I go wrong somewhere? What do I do next?

- Precalculus/Trig -
**Steve**, Friday, August 15, 2014 at 2:56pm(cos+1)/sin^3 = csc/(1-cos)

multiply by (1-cos)

(1+cos)(1-cos)/sin^3 = csc = 1/sin

(1-cos^2)/sin^2 = 1

sin^2/sin^2 = 1

1 = 1

(sin+cos)(tan+cot) = sec+csc

sin*tan + cos*tan + sin*cot + cos*cot = sec+csc

sin^2/cos + sin + cos + cos^2/sin = sec+csc

(sin^2+cos)/cos + (sin^2+cos^2)/sin = sec+csc

1/cos + 1/sin = sec+csc

sec+csc = sec+csc

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