Show that cosec(2x) + cot(2x) = cot(x)
cosec(2x) + cot(2x)
CONVERT ALL COSEC/COT/SEC FUNCTIONS INTO FUNCTIONS USING SIN/TAN/COS
= 1 / (sin2x) + cos(2x) / sin(2x)
COMBINE THE TWO FRACTIONS INTO ONE
= [1+cos(2x)] / [sin(2x)]
USE COS AND SIN DOUBLE ANGLE FORMULA
a) COS(2X) = 2COS2(X) - 1
b) SIN(2X) = 2SIN(X)COS(X)
= [1+2cos2(x)-1] / [2sin(x)cos(x)]
COLLECT LIKE TERMS
= [2cos2(x)] / [2sin(x)cos(x)]
DIVIDE BY COS(X) ON BOTH BOTTOM AND TOP OF FRACTION
= [cos(x)] / [sin(x)]
USE IDENTITY [SIN(X)] / [COS(X)] = TAN(X)
= [1] / [tan(x)]
USE IDENTITY [1] / [TAN(X)] = COT(X)
= cot(x)
DK
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