sederhanakan (cot x - tan x)/(cos x - sin x)
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Step-by-step explanation:
(Cotx - Tanx) / (Cosx - Sinx)
=> [(Cosx/Sinx) - (Sinx/Cos)] / (Cosx - Sinx)
//SinxCosx is the LCM for the numerator
=> [Cos²x - Sin²x / CosxSinx] / (Cosx - Sinx)
=> Cos²x - Sin²x / CosxSinx (Cosx - Sinx)
//Numerator is of form a² - b². we know that a² - b² = (a + b)(a - b)
=> (Cosx + Sinx) (Cosx - Sinx) / CosxSinx (Cosx - Sinx)
=> Cosx + Sinx / CosxSinx
=> Cosx/CosxSinx + Sinx/CosxSinx
=> 1/Sinx + 1 / Cosx
=> Cosecx + Secx.
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