P2 trig proofs Watch

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jazzyj
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#1
Report Thread starter 14 years ago
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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
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kikzen
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(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
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mikesgt2
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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)
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Fermat
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(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)
=========
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Fermat
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(Original post by jazzyj)
hey...i'm having trouble proving these. any help much appreciated! thanks x

4) tan2xsecx = 2sinxsec2x
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kikzen
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my way was easier
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jazzyj
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#7
Report Thread starter 14 years ago
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thank u all so much!
xx
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Fermat
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(Original post by kikzen)
my way was easier
No 4 ?
Yeah, nice one
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