lim x tends to pi/2 tan 3x / tan x

Consider the expression,limxπ2tan3xtanxUse trigonometric identity:tan3x=3tanx-tan3x3-3tan2xTherefore, above expression reduces tolimxπ2tan3xtanx=limxπ23tanx-tan3x3-3tan2xtanx=limxπ23tanx-tan3xtanx3-3tan2x=limxπ23-tan2x3-3tan2x=limxπ23-sin2xcos2x3-3sin2xcos2x=limxπ23cos2x-sin2x3cos2x-3sin2xPut the value of limit in the expression,=3cos2π2-sin2π23cos2π2-3sin2π2Since, cosπ2=0 and sinπ2=1=30-1230-312=-1-3=13

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Infinity
 
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