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Leekey
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#1
Report Thread starter 18 years ago
#1
I have finally brought myself round to doing a bit of work during the hols and am struggling to prove the following trig identities:

1) (1 - sinX) / (cosX) = (1) / (secX + tanX)


2) cosecX - sinX = cotXcosX

Any help would be much appreciated, I keep running into brickwalls with it!!!

Particularly looking in the direction of Bicnee who I know can do this!!!
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Ralfskini
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#2
Report 18 years ago
#2
(Original post by Leekey)
I have finally brought myself round to doing a bit of work during the hols and am struggling to prove the following trig identities:

1) (1 - sinX) / (cosX) = (1) / (secX + tanX)


2) cosecX - sinX = cotXcosX

Any help would be much appreciated, I keep running into brickwalls with it!!!

Particularly looking in the direction of Bicnee who I know can do this!!!
In reply to the 2).


cotxcosx = (cosx/sinx).cosx = cos^x/sinx = (1-sin^x)/sinx


=1/sinx - sin^x/sinx = cosecx - sinx.
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Ralfskini
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#3
Report 18 years ago
#3
(Original post by Ralfskini)
In reply to the 2).


cotxcosx = (cosx/sinx).cosx = cos^x/sinx = (1-sin^x)/sinx


=1/sinx - sin^x/sinx = cosecx - sinx.

Ive done 1). now, too:

1/(secx + tanx) = (secx - tanx)/((secx+tanx)(secx-tanx))

=(secx - tanx)/ (sec(^2)x - tan(^2)x)

=secx - tanx (using 1 + tan(^2)x = sec(^2)x)

= 1/cosx - sinx/cosx

=(1 - sinx)/(cosx).
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Leekey
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#4
Report Thread starter 18 years ago
#4
Thankyou sooo much!!!

*gives copious amounts of rep*
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