Solve for x, sin[cot-1(x+1)]=cos(tan-1x)?


Asked by sweety | 15th Nov, 2015, 07:59: PM

Expert Answer:

G i v e n space t h a t space sin open square brackets c o t to the power of negative 1 end exponent open parentheses x plus 1 close parentheses close square brackets equals cos open parentheses tan to the power of negative 1 end exponent x close parentheses... open parentheses 1 close parentheses W e space k n o w space t h a t comma c o t to the power of negative 1 end exponent A equals sin to the power of negative 1 end exponent fraction numerator 1 over denominator square root of 1 plus A squared end root end fraction H e r e comma space A equals x plus 1 A p p l y i n g space t h i s space i d e n t i t y space i n space e q u a t i o n space open parentheses 1 close parentheses comma space w e space h a v e comma space s i n open square brackets s i n to the power of negative 1 end exponent fraction numerator 1 over denominator square root of 1 plus open parentheses 1 plus x close parentheses squared end root end fraction close square brackets equals c o s open parentheses t a n to the power of negative 1 end exponent x close parentheses.... open parentheses 2 close parentheses A l s o space w e space k n o w space t h a t comma space tan to the power of negative 1 end exponent A equals cos to the power of negative 1 end exponent fraction numerator 1 over denominator square root of 1 plus A squared end root end fraction H e r e comma space A equals x A p p l y i n g space t h i s space i d e n t i t y space i n space e q u a t i o n space open parentheses 2 close parentheses comma space w e space h a v e comma space s i n open square brackets s i n to the power of negative 1 end exponent fraction numerator 1 over denominator square root of 1 plus open parentheses 1 plus x close parentheses squared end root end fraction close square brackets equals c o s open parentheses c o s to the power of negative 1 end exponent fraction numerator 1 over denominator square root of 1 plus x squared end root end fraction close parentheses rightwards double arrow fraction numerator 1 over denominator square root of 1 plus open parentheses 1 plus x close parentheses squared end root end fraction equals fraction numerator 1 over denominator square root of 1 plus x squared end root end fraction S q u a r i n g space a n d space r e c i p r o c a t i n g space b o t h space t h e space s i d e s comma space w e space h a v e comma 1 plus open parentheses 1 plus x close parentheses squared equals 1 plus x squared rightwards double arrow 1 plus 1 plus x squared plus 2 x equals 1 plus x squared rightwards double arrow 1 plus 2 x equals 0 rightwards double arrow x equals fraction numerator negative 1 over denominator 2 end fraction

Answered by Vimala Ramamurthy | 16th Nov, 2015, 09:00: AM