s o l v e space f o r space x space : space space space space space space space space space space space space space space space space space space space space space space sin to the power of minus 1 end exponent open parentheses 1 minus x close parentheses space minus space 2 sin to the power of minus 1 end exponent open parentheses x close parentheses space equals space straight pi divided by 2

Asked by Lochana Jayachandran | 5th Oct, 2014, 07:29: 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 : sin to the power of minus 1 end exponent open parentheses 1 minus x close parentheses minus 2 sin to the power of minus 1 end exponent open parentheses x close parentheses equals straight pi over 2 rightwards double arrow sin to the power of minus 1 end exponent open parentheses 1 minus x close parentheses equals straight pi over 2 plus 2 sin to the power of minus 1 end exponent open parentheses x close parentheses rightwards double arrow 1 minus x equals sin open parentheses straight pi over 2 plus 2 sin to the power of minus 1 end exponent open parentheses x close parentheses close parentheses rightwards double arrow 1 minus x equals cos open square brackets 2 sin to the power of minus 1 end exponent open parentheses x close parentheses close square brackets... open parentheses 1 close parentheses W e space k n o w space t h a t comma space 2 sin to the power of minus 1 end exponent open parentheses x close parentheses equals cos to the power of minus 1 end exponent open parentheses 1 minus 2 x squared close parentheses T h u s comma space e q u a t i o n space left parenthesis 1 right parenthesis comma space b e c o m e s comma 1 minus x equals cos open square brackets cos to the power of minus 1 end exponent open parentheses 1 minus 2 x squared close parentheses close square brackets rightwards double arrow 1 minus x equals 1 minus 2 x squared rightwards double arrow x equals 2 x squared rightwards double arrow x open parentheses 2 x minus 1 close parentheses equals 0 rightwards double arrow x equals 0 space o r space x equals 1 half L e t space u s space s u b s t i t u t e space x equals 1 half space i n space t h e space g i v e n space e q u a t i o n. T h u s comma space g i v e n space e q u a t i o n space b e c o m e s comma L H S equals sin to the power of minus 1 end exponent open parentheses 1 minus x close parentheses minus 2 sin to the power of minus 1 end exponent x equals sin to the power of minus 1 end exponent open parentheses 1 minus 1 half close parentheses minus 2 sin to the power of minus 1 end exponent open parentheses 1 half close parentheses equals sin to the power of minus 1 end exponent open parentheses 1 half close parentheses minus 2 sin to the power of minus 1 end exponent open parentheses 1 half close parentheses equals minus sin to the power of minus 1 end exponent open parentheses 1 half close parentheses equals minus straight pi over 6 not equal to R H S T h u s comma space i t space i s space c l e a r space t h a t space x equals 1 half space i s space n o t space a space r o o t space o f space t h e space g i v e n space e q u a t i o n. T h u s comma space x equals 0 space i s space t h e space s o l u t i o n space o f space t h e space g i v e n space e q u a t i o n.

Answered by Vimala Ramamurthy | 6th Oct, 2014, 09:13: AM

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