Given \cos(a)+\cos(b)=1, prove that 1−s^2−t^2−3s^2t^2=0, where s=\tan(\frac{a}{2}) and t=\tan(\frac{b}{2})

hadejada7x 2022-01-15 Answered
Given cos(a)+cos(b)=1, prove that 1s2t23s2t2=0, where s=tan(a2) and t=tan(b2)
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Answers (3)

Elaine Verrett
Answered 2022-01-16 Author has 41 answers
Alternatively:
cosa=2cos2a21
cos2a2=11+tan2a2=11+s2
cosa+cosb=2cos2a2+2cos2b22=
21+s2+21+t22=1
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RizerMix
Answered 2022-01-20 Author has 438 answers
1t21+t2+1s21+s2=1 1+s2t2s2t2+1+t2s2s2t2=1+s2+t2+s2t2 1s2t23s2t2=0
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alenahelenash
Answered 2022-01-24 Author has 343 answers
Hint: 1s21+s2+1t21+t2=1 1s21+s2=11t21+t2 (1s2)(1+t2)=2t2(1+s2)
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