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jimC
07-17-2008, 09:18 PM
theta=(T) degrees=(D)
1)prove:tan(T)-cot(T)/tan(T)+cot(T)=2sin^2(T) - 1
2)prove:1-cos(T)/sin(T)=sin(T)/1+cos(T)
3)prove:1-tan^2(T)/1+tan^2(T)=1 - 2sin^2(T)

san2612
03-25-2010, 11:55 AM
Though I don't know much about math sybols in English, it's my answer to the exercise:
1,
tan(T)-cot(T)/ [tan(T)+cot(T)]
= sin^2(T)-cos^2(T)/ [sin^2(T)+cos^2(T)]
= sin^2(T)- cos^2(T) = 2sin^2(T) - 1

2,
1-cos(T)/sin(T)
= 1 - cos^2(T)/ [sin (T). (1+cos(T)]
= sin^2(T)/ [sin (T). (1+cos(T)]
= sin(T)/[1+cos(T)]

3,
1-tan^2(T)/1+tan^2(T)
= cos^2(T) - sin^2 (T)
= 1 - 2sin^2(T)