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sinC + cosC - 1 --------------- ............................................... = sinC - cosC + 1 |
cosC ------- sinC + 1 |
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[sinC + (cosC - 1)] [sinC + (cosC - 1)] --------------------------------------- [sinC - (cosC - 1)] [sinC + (cosC - 1)] sin^2C + sinCcosC - sinC + sinCcosC + cos^2C - cosC - sinC - cosC + 1 --------------------------------------------------------------------- sin^2C + sinCcosC - sinC - sinCcosC - cos^2C + cosC + sinC + cosC - 1 which simplifies to... 2 + 2sinCcosC - 2sinC - 2cosC ----------------------------- sin^2C - cos^2C + 2cosC - 1 2(cosC - 1)(sinC - 1) --------------------- 2(cosC - cos^2C) which then simplifies to... 1 - sinC --------- cosC multiply both sides by cosC to get... cosC(1 - sinC) -------------- cos^2C and since cos^2C = (1 - sin^2C), we stick this into the denominator... cosC(1 - sinC) -------------- (1 - sin^2C) and since (1 - sin^2C) = (1 + sinC)(1 - sinC), we can elinate (1 - sinC) from both sides and obtain: cosC ------ 1 + sinC |