# P2 trig proofsWatch

This discussion is closed.
#1
hey...i'm having trouble proving these. any help much appreciated! thanks x

1) [ (1 + sinx)/cosx ]^2 + [ (1 - sinx)/cosx ]^2 = 2 + 4tan^2x

2) (tanx + secx)(cotx + cosecx) = (1 + secx)(1 + cosecx)

3) cotx - tanx = 2cot2x

4) tan2xsecx = 2sinxsec2x
0
14 years ago
#2
(Original post by jazzyj)
hey...i'm having trouble proving these. any help much appreciated! thanks x

1) [ (1 + sinx)/cosx ]^2 + [ (1 - sinx)/cosx ]^2 = 2 + 4tan^2x

2) (tanx + secx)(cotx + cosecx) = (1 + secx)(1 + cosecx)

3) cotx - tanx = 2cot2x

4) tan2xsecx = 2sinxsec2x
0
14 years ago
#3
3) 2cot2x = 2cos2x/sin2x = 2[ cos^2(x) - sin^2(x) ]/[ 2sin(x)cos(x) ] = [ cos^2(x) - sin^2(x) ]/[ sin(x)cos(x) ] = [ cos^2(x) ]/[ sin(x)cos(x) ] - [ sin^2(x) ]/[ sin(x)cos(x) ] = cos(x)/sin(x) - sin(x)/cos(x) = cot(x) - tan(x)
0
14 years ago
#4
(Original post by jazzyj)
hey...i'm having trouble proving these. any help much appreciated! thanks x

1) [ (1 + sinx)/cosx ]^2 + [ (1 - sinx)/cosx ]^2 = 2 + 4tan^2x
[ (1 + sinx)/cosx ]^2 + [ (1 - sinx)/cosx ]^2

expand the brackets,

(1+2sinx + sin²x + 1 - 2sinx + sin²x)/cos²x
2(1 + sim²x)/cos²x
2(sec²x + tan²x)
2(1 + tan²x + tan²x) (1+tan²x = sec²x)
2(1 + 2tan²x)
=========
0
14 years ago
#5
(Original post by jazzyj)
hey...i'm having trouble proving these. any help much appreciated! thanks x

4) tan2xsecx = 2sinxsec2x
0
14 years ago
#6
my way was easier
0
#7
thank u all so much!
xx
0
14 years ago
#8
(Original post by kikzen)
my way was easier
No 4 ?
Yeah, nice one
0
X
new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• University of East Anglia
All Departments Open 13:00-17:00. Find out more about our diverse range of subject areas and career progression in the Arts & Humanities, Social Sciences, Medicine & Health Sciences, and the Sciences. Postgraduate
Wed, 30 Jan '19
• Aston University
Wed, 30 Jan '19
• Solent University
Sat, 2 Feb '19

### Poll

Join the discussion

Remain (1065)
79.01%
Leave (283)
20.99%