Buktikan bahwa sin theta/1-cos theta + tan theta /1 + cos theta = sec theta × cosec theta + cot theta?

Sin theta/1-cos theta + tan theta / 1+cos theta = sec theta × cosec theta + cot theta

Bukti

Sinθ/(1 – cosθ) + Tanθ/(1 + cosθ) = Secθ.Cos + Cotθ

Mari kita mulai dengan LHS

= Sinθ/(1 – cosθ) + Tanθ/(1 + cosθ)

= (sinθ(1 + cosθ) + Tanθ(1-Cosθ))/(1 – Cos²θ)

= (sinθ(1 + cosθ) + (Tanθ – Sinθ)) /Sin²θ

= ( 1 + cosθ + 1/Cosθ – 1)/Sinθ

= (cosθ + 1/Cosθ)/Sinθ

= 1/CosθSinθ + cosθ/Sinθ

= Secθ.Cosecθ + Cotθ

= RHS

Maka Terbukti

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