Saturday

December 20, 2014

December 20, 2014

Posted by **Jay** on Sunday, December 4, 2011 at 11:42am.

1.1+sinx/1-sinx=cscx+1/cscx-1

2.tanx+sinx/1+cosx=tanx

3.sec^2x/sin^2x=1/sin^2x+1/cos^2x

4.tan^2x/1+tan^2x=1-cos^2x

5.sinx-sin^3x/cos^3x=tanx

- trig -
**Reiny**, Sunday, December 4, 2011 at 11:50amMy method

1. start with the more complicate looking side

2. change everything to sines and cosines, unless I recognize an obvious identity

I will do #2 for you

LS = (tanx + sinx)/(1 + cosx)

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

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

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

= sinx/cosx

= tanx

= RS

by "obvious identity" I notice in #4 that we have the expression

1 + tan^2x

from the Pythagorean identities

1 + tan^2x = sec^2x

so #4

LS = tan^2x/(1+tan^2)

= tan^2x/sec^2x

= tan^2x cos^2x

= sin^2x/cos^2x (cos^2x) = sin^2x

= 1 - cos^2x

= RS

**Answer this Question**

**Related Questions**

Trigonometry - Prove the following trigonometric identities. please give a ...

Precalculus/Trig - I can't seem to prove these trig identities and would really ...

Trigonometry. - ( tanx/1-cotx )+ (cotx/1-tanx)= (1+secxcscx) Good one! ...

Trig Help - Prove the following: [1+sinx]/[1+cscx]=tanx/secx =[1+sinx]/[1+1/sinx...

Math (trigonometric identities) - I was given 21 questions for homework and I ...

trig - express this in sinx (1/ cscx + cotx )+ (1/cscx- cotx) i got 2sinx is ...

Calculus - Q: If y=sinx/(1+tanx), find value of x not greater than pi, ...

Trigonometry - Simplify #1: cscx(sin^2x+cos^2xtanx)/sinx+cosx = cscx((1)tanx)/...

Math 12 - Simplify #1: cscx(sin^2x+cos^2xtanx)/sinx+cosx = cscx((1)tanx)/sinx+...

Trigonometry Check - Simplify #3: [cosx-sin(90-x)sinx]/[cosx-cos(180-x)tanx] = [...