Proving \frac{1}{(\tan(\frac x2)+1)^2 \cos^2(\frac x2)}=\frac{1}{1+\sin x}

PEEWSRIGWETRYqx 2022-01-16 Answered
Proving 1(tan(x2)+1)2cos2(x2)=11+sinx
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Expert Answer

Barbara Meeker
Answered 2022-01-17 Author has 38 answers
1(tanx2+1)2cos2x2=1(tan2x2+2tanx2+1)cos2x2
=1sin2x2+2sinx2cosx2+cos2x2=11+2sinx2cosx2=11+sinx
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Navreaiw
Answered 2022-01-18 Author has 34 answers
Let tanx2=t
So we have
1+t2(t+1)2==11+2t1+t2
Now use Weierstrass substitution
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