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Ques no 33

Asked by chandanbr6004 8th November 2017, 9:42 PM
Answered by Expert
Answer:
begin mathsize 16px style Use space Polar space coordinates space here.
straight a equals rcosθ space and space straight y equals rsinθ
tanθ equals sinθ over cosθ equals straight b over straight a
rightwards double arrow space straight a plus ib equals straight r open parentheses cosθ plus isinθ close parentheses
rightwards double arrow straight a minus ib equals straight r open parentheses cosθ minus isinθ close parentheses
tan open square brackets straight i cross times log open parentheses fraction numerator straight a minus ib over denominator straight a plus ib end fraction close parentheses close square brackets
tan open square brackets straight i cross times log open parentheses fraction numerator straight r open parentheses cosθ minus isinθ close parentheses over denominator straight r open parentheses cosθ plus isinθ close parentheses end fraction close parentheses close square brackets

tan open square brackets straight i cross times log open parentheses fraction numerator open parentheses cosθ minus isinθ close parentheses over denominator open parentheses cosθ plus isinθ close parentheses end fraction close parentheses close square brackets
tan open square brackets straight i cross times log open parentheses straight e to the power of negative ix end exponent over straight e to the power of ix close parentheses close square brackets
tan open square brackets straight i cross times log open parentheses straight e to the power of negative 2 ix end exponent close parentheses close square brackets
tan open square brackets straight i cross times open parentheses negative 2 ix close parentheses close square brackets
tan open square brackets negative 2 straight i squared straight x close square brackets
tan 2 straight x
Use space formula space tan 2 straight x equals fraction numerator 2 tanx over denominator straight a minus tan squared straight x end fraction
and space simplify space you space will space get space fraction numerator 2 ab over denominator straight a squared minus straight b squared end fraction end style
Answered by Expert 11th December 2017, 2:04 PM
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