how to convert this to cos1000pit5sin100pit Cos1000 pi t Cos

how to convert this to cos[1000pit-5sin(100pit)]

Cos[1000 pi t] Cos[5 Sin [100 pi t]] + Sin[1000 pi t] Sin[5 Sin[100 pi t]] how to convert this to cos[1000pi t - 5sin(100pi t)

Solution

cos[1000pit]cos[5sin[100pit]] + sin[1000pit]sin[5sin[100pit]]

Use the formula : cos(x -y) = cosxcosy +sinxsiny

cos[1000pit]cos[5sin[100pit]] + sin[1000pit]sin[5sin[100pit]]

= cos[ 1000pi*t -5sin[100pi*t]]

how to convert this to cos[1000pit-5sin(100pit)] Cos[1000 pi t] Cos[5 Sin [100 pi t]] + Sin[1000 pi t] Sin[5 Sin[100 pi t]] how to convert this to cos[1000pi t

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