solve for x:-
 
sin[2 cos-1 {cot(2 tan-1 x)}] = 0
 
 
 
 
along with explanation

Asked by yash.bisht9910 | 27th Apr, 2015, 05:21: PM

Expert Answer:

C o n s i d e r space t h e space g i v e n space e q u a t i o n colon sin open square brackets 2 cos to the power of negative 1 end exponent open curly brackets c o t open parentheses 2 tan to the power of negative 1 end exponent x close parentheses close curly brackets close square brackets equals 0 W e space k n o w space t h a t space 2 tan to the power of negative 1 end exponent x equals tan to the power of negative 1 end exponent fraction numerator 2 x over denominator 1 minus x squared end fraction T h u s comma space r e w r i t i n g space t h e space g i v e n space e q u a t i o n comma space w e space h a v e comma sin open square brackets 2 cos to the power of negative 1 end exponent open curly brackets c o t open parentheses tan to the power of negative 1 end exponent fraction numerator 2 x over denominator 1 minus x squared end fraction close parentheses close curly brackets close square brackets equals 0 rightwards double arrow sin open square brackets 2 cos to the power of negative 1 end exponent open curly brackets c o t open parentheses c o t to the power of negative 1 end exponent fraction numerator 1 minus x squared over denominator 2 x end fraction close parentheses close curly brackets close square brackets equals 0 space space space space space open square brackets because tan to the power of negative 1 end exponent x equals c o t to the power of negative 1 end exponent 1 over x close square brackets rightwards double arrow sin open square brackets 2 cos to the power of negative 1 end exponent open curly brackets fraction numerator 1 minus x squared over denominator 2 x end fraction close curly brackets close square brackets equals 0 space space space space space space space space space space space space space space space space space space space space space space space open square brackets because c o t open parentheses c o t to the power of negative 1 end exponent x close parentheses equals x close square brackets rightwards double arrow sin open square brackets sin to the power of negative 1 end exponent open square brackets 2 open curly brackets fraction numerator 1 minus x squared over denominator x end fraction close curly brackets square root of 1 minus open curly brackets fraction numerator 1 minus x squared over denominator 2 x end fraction close curly brackets squared end root close square brackets close square brackets equals 0 space space space space space space space space space space space space space space open square brackets because 2 cos to the power of negative 1 end exponent x equals sin to the power of negative 1 end exponent open parentheses 2 x square root of 1 minus x squared end root close parentheses close square brackets rightwards double arrow 2 open curly brackets fraction numerator 1 minus x squared over denominator x end fraction close curly brackets square root of 1 minus open curly brackets fraction numerator 1 minus x squared over denominator 2 x end fraction close curly brackets squared end root equals 0 space space space rightwards double arrow space space fraction numerator 1 minus x squared over denominator x end fraction equals 0 space o r space square root of 1 minus open curly brackets fraction numerator 1 minus x squared over denominator 2 x end fraction close curly brackets squared end root equals 0 rightwards double arrow space space 1 minus x squared equals 0 space o r space open curly brackets fraction numerator 1 minus x squared over denominator 2 x end fraction close curly brackets squared equals 1 rightwards double arrow x equals plus-or-minus 1 space o r space open parentheses 1 minus x squared close parentheses squared equals 4 x squared rightwards double arrow x equals plus-or-minus 1 space o r space open parentheses 1 minus x squared close parentheses squared minus open parentheses 2 x close parentheses squared equals 0 rightwards double arrow x equals plus-or-minus 1 space o r open square brackets space open parentheses 1 minus x squared close parentheses minus open parentheses 2 x close parentheses close square brackets open square brackets space open parentheses 1 minus x squared close parentheses plus open parentheses 2 x close parentheses close square brackets equals 0 rightwards double arrow x equals plus-or-minus 1 space o r open square brackets space open parentheses 1 minus x squared close parentheses minus open parentheses 2 x close parentheses close square brackets equals 0 space o r space open square brackets space open parentheses 1 minus x squared close parentheses plus open parentheses 2 x close parentheses close square brackets equals 0 rightwards double arrow x equals plus-or-minus 1 space o r space x squared minus 2 x minus 1 equals 0 space o r space x squared plus 2 x minus 1 equals 0 rightwards double arrow x equals plus-or-minus 1 space o r space x equals negative 1 plus-or-minus square root of 2 comma space x equals 1 plus-or-minus square root of 2

Answered by Vimala Ramamurthy | 28th Apr, 2015, 09:27: AM