Get the answer to "Proving 1(tan⁡(x2)+1)2cos2(x2)=11+sin⁡x"

PEEWSRIGWETRYqx

Answered question

2022-01-16

Proving

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

Barbara Meeker

Beginner2022-01-17Added 38 answers

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

= \frac{1}{\sin^{2} \frac{x}{2} + 2 \sin \frac{x}{2} \cos \frac{x}{2} + \cos^{2} \frac{x}{2}} = \frac{1}{1 + 2 \sin \frac{x}{2} \cos \frac{x}{2}} = \frac{1}{1 + \sin x}

Navreaiw

Beginner2022-01-18Added 34 answers

Let

\tan \frac{x}{2} = t

So we have

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

Now use Weierstrass substitution

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