1.

Under root 1-cosx upon under root 1+cosx =tanx /2​

Answer»

Step-by-step explanation:

Since you want to finish up with tan(X/2)tan⁡(x/2), recall the famous, important and useful formulas

[math] \ SIN x = \ dfrac {2T} {1 + t ^ 2} \ qquad \ COS x = \ dfrac {1-t ^ 2} {1 + t ^ 2} [/ math]

where t=tan(x/2)t=tan⁡(x/2). Then

[math] 1- \ cos x = 1- \ dfrac {1-t ^ 2} {1 + t ^ 2} = \ dfrac {1 + t ^ 2–1 + t ^ 2} {1 + t ^ 2} = \ dfrac {2t ^ 2} {1 + t ^ 2} [/ math]

and

[math] 1+ \ cos x = 1 + \ dfrac {1-t ^ 2} {1 + t ^ 2} = \ dfrac {1 + t ^ 2 + 1-t ^ 2} {1 + t ^ 2} = \ dfrac {2} {1 + t ^ 2} [/ math]

so that

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