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Help trig identities

Help! Can anyone guide me through this trig identity, much appreciated (1-tan^2theta)/(1+tan^2theta)=1-2sin^2theta. Thnks
Reply 1
Avatar for TeeEm
TeeEm
19
Original post by James_pa
Help! Can anyone guide me through this trig identity, much appreciated (1-tan^2theta)/(1+tan^2theta)=1-2sin^2theta. Thnks


multiply it out
change to sines and cosines
add the 2 bits (common denominator)
and finish off
Reply 2
Avatar for Notnek
Notnek
21
Original post by James_pa
Help! Can anyone guide me through this trig identity, much appreciated (1-tan^2theta)/(1+tan^2theta)=1-2sin^2theta. Thnks

An alternative method:

1+tan2x≡sec2x1+tan^2 x \equiv sec^2 x

Then split the fraction, cancel and use another identity.
Reply 3
Avatar for davros
davros
16
Original post by James_pa
Help! Can anyone guide me through this trig identity, much appreciated (1-tan^2theta)/(1+tan^2theta)=1-2sin^2theta. Thnks


Another method:

multiply top and bottom by cos^2 (theta). The denominator should be easily recognizable from a standard identity. The numerator can be rearranged fairly simply using the same identity :smile:
Reply 4
Avatar for James_pa
James_pa
OP
6
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