Proving $\frac{1}{{(\mathrm{tan}\left(\frac{x}{2}\right)+1)}^{2}{\mathrm{cos}}^{2}\left(\frac{x}{2}\right)}=\frac{1}{1+\mathrm{sin}x}$

PEEWSRIGWETRYqx
2022-01-16
Answered

Proving $\frac{1}{{(\mathrm{tan}\left(\frac{x}{2}\right)+1)}^{2}{\mathrm{cos}}^{2}\left(\frac{x}{2}\right)}=\frac{1}{1+\mathrm{sin}x}$

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Barbara Meeker

Answered 2022-01-17
Author has **38** answers

Navreaiw

Answered 2022-01-18
Author has **34** answers

Let $\mathrm{tan}\frac{x}{2}=t$

So we have

$\frac{1+{t}^{2}}{{(t+1)}^{2}}=\dots =\frac{1}{1+\frac{2t}{1+{t}^{2}}}$

Now use Weierstrass substitution

So we have

Now use Weierstrass substitution

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