Asked by hasanali.ali986 | 25th May, 2015, 07:40: PM

Expert Answer:

left parenthesis 7 right parenthesis space S o l v e space f o r space x colon sin to the power of negative 1 end exponent x plus sin to the power of negative 1 end exponent 2 x equals straight pi over 3 rightwards double arrow sin to the power of negative 1 end exponent x plus sin to the power of negative 1 end exponent 2 x equals straight pi over 3 rightwards double arrow sin to the power of negative 1 end exponent open parentheses x square root of 1 minus 4 x squared end root plus 2 x square root of 1 minus x squared end root close parentheses equals straight pi over 3 rightwards double arrow open parentheses x square root of 1 minus 4 x squared end root plus 2 x square root of 1 minus x squared end root close parentheses equals sin straight pi over 3 rightwards double arrow open parentheses x square root of 1 minus 4 x squared end root plus 2 x square root of 1 minus x squared end root close parentheses equals fraction numerator square root of 3 over denominator 2 end fraction rightwards double arrow x square root of 1 minus 4 x squared end root equals fraction numerator square root of 3 over denominator 2 end fraction minus 2 x square root of 1 minus x squared end root rightwards double arrow x squared open parentheses 1 minus 4 x squared close parentheses equals 3 over 4 plus 4 x squared left parenthesis 1 minus x squared right parenthesis minus 2 x square root of 3 left parenthesis 1 minus x squared right parenthesis end root rightwards double arrow x squared minus 4 x to the power of 4 equals fraction numerator 3 plus 16 x squared left parenthesis 1 minus x squared right parenthesis minus 8 x square root of 3 left parenthesis 1 minus x squared right parenthesis end root over denominator 4 end fraction rightwards double arrow 4 x squared minus 16 x to the power of 4 equals 3 plus 16 x squared minus 16 x to the power of 4 minus 8 x square root of 3 left parenthesis 1 minus x squared right parenthesis end root rightwards double arrow negative 12 x squared minus 3 equals negative 8 x square root of 3 left parenthesis 1 minus x squared right parenthesis end root rightwards double arrow 144 x to the power of 4 plus 9 plus 2 cross times 3 cross times 12 x squared equals 64 x squared open parentheses 3 minus 3 x squared close parentheses rightwards double arrow 144 x to the power of 4 plus 9 plus 72 x squared equals 192 x squared minus 192 x to the power of 4 rightwards double arrow 144 x to the power of 4 plus 192 x to the power of 4 plus 72 x squared minus 192 x squared plus 9 equals 0 rightwards double arrow 336 x to the power of 4 minus 120 x squared plus 9 equals 0 rightwards double arrow 112 x to the power of 4 minus 40 x squared plus 3 equals 0 rightwards double arrow 112 x to the power of 4 minus 28 x squared minus 12 x squared plus 3 equals 0 rightwards double arrow 28 x squared left parenthesis 4 x squared minus 1 right parenthesis minus 3 left parenthesis 4 x squared minus 1 right parenthesis equals 0 rightwards double arrow left parenthesis 28 x squared minus 3 right parenthesis left parenthesis 4 x squared minus 1 right parenthesis equals 0 rightwards double arrow x squared equals 3 over 28 comma 1 fourth therefore space x equals 1 half comma square root of 3 over 28 end root P l e a s e space t y p e space e a c h space o f space t h e space q u e s t i o n s space s e p a r a t e l y.

Answered by Prasenjit Paul | 26th May, 2015, 11:21: AM