Given cos⁡(a)+cos⁡(b)=1, prove that 1−s2−t2−3s2t2=0, where s=tan⁡(a2) and t=tan⁡(b2)

hadejada7x

hadejada7x

Answered

2022-01-15

Given cos(a)+cos(b)=1, prove that 1s2t23s2t2=0, where s=tan(a2) and t=tan(b2)

Answer & Explanation

Elaine Verrett

Elaine Verrett

Expert

2022-01-16Added 41 answers

Alternatively:
cosa=2cos2a21
cos2a2=11+tan2a2=11+s2
cosa+cosb=2cos2a2+2cos2b22=
21+s2+21+t22=1
RizerMix

RizerMix

Expert

2022-01-20Added 437 answers

1t21+t2+1s21+s2=1 1+s2t2s2t2+1+t2s2s2t2=1+s2+t2+s2t2 1s2t23s2t2=0
alenahelenash

alenahelenash

Expert

2022-01-24Added 366 answers

Hint: 1s21+s2+1t21+t2=1 1s21+s2=11t21+t2 (1s2)(1+t2)=2t2(1+s2)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?