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Can you provide a shorter solution to this question 

 

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Asked by Varsneya Srinivas 21st February 2018, 10:46 AM
Answered by Expert
Answer:
begin mathsize 16px style xy plus yz plus zx equals 1
If space you space take space straight x equals tanA comma space straight y equals tanB comma space straight z equals tanC space then
tan space open parentheses straight A plus straight B plus straight C close parentheses equals tan open square brackets open parentheses straight A plus straight B close parentheses plus straight C close square brackets equals fraction numerator tan left parenthesis straight A plus straight B right parenthesis plus tanC over denominator 1 minus tan left parenthesis straight A plus straight B right parenthesis tanC end fraction
Using space formula space again space for space tan left parenthesis straight A plus straight B right parenthesis
you space get
fraction numerator tanA plus tanB plus tanC minus tanAtanBtanC over denominator 1 minus tanAtanB minus tanBtanC minus tanAtanC end fraction
as space xy plus yz plus zx equals 1 rightwards double arrow tanAtanB plus tanBtanC plus tanAtanC equals 1
rightwards double arrow tan space open parentheses straight A plus straight B plus straight C close parentheses equals infinity
straight A plus straight B plus straight C space is space multiple space of space straight pi over 2

tan 2 straight A plus tan 2 straight B plus tan 2 straight C equals tan 2 straight A plus tan 2 straight B plus tan 2 straight C
tan 2 straight x equals fraction numerator 2 tanx over denominator 1 minus tan squared straight x end fraction
Using space this space formula space you space can space prove space it.
space

















end style
Answered by Expert 21st February 2018, 11:23 AM
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