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CBSE Class 12-science Answered

Sin-1(1-x)-2sin-1x==π/2
Asked by pramodtalukdar | 27 Oct, 2016, 02:41: PM
answered-by-expert Expert Answer
begin mathsize 16px style sin to the power of negative 1 end exponent left parenthesis 1 minus straight x right parenthesis minus 2 sin to the power of negative 1 end exponent straight x equals straight pi over 2
rightwards double arrow sin to the power of negative 1 end exponent left parenthesis 1 minus straight x right parenthesis equals straight pi over 2 plus 2 sin to the power of negative 1 end exponent straight x
rightwards double arrow left parenthesis 1 minus straight x right parenthesis equals sin open parentheses straight pi over 2 plus 2 sin to the power of negative 1 end exponent straight x close parentheses
rightwards double arrow left parenthesis 1 minus straight x right parenthesis equals cos open parentheses 2 sin to the power of negative 1 end exponent straight x close parentheses
rightwards double arrow left parenthesis 1 minus straight x right parenthesis equals cos open square brackets cos to the power of negative 1 end exponent open parentheses 1 minus 2 straight x squared close parentheses close square brackets
rightwards double arrow left parenthesis 1 minus straight x right parenthesis equals 1 minus 2 straight x squared
rightwards double arrow 2 straight x squared minus straight x equals 0
rightwards double arrow straight x left parenthesis 2 straight x minus 1 right parenthesis equals 0
rightwards double arrow straight x equals 0 space or space 2 straight x minus 1 equals 0
rightwards double arrow straight x equals 0 space space space or space space space straight x equals 1 half
If space straight x equals 1 half comma
LHS equals sin to the power of negative 1 end exponent left parenthesis 1 minus straight x right parenthesis minus 2 sin to the power of negative 1 end exponent straight x equals sin to the power of negative 1 end exponent open parentheses 1 half close parentheses minus 2 sin to the power of negative 1 end exponent open parentheses 1 half close parentheses equals negative straight pi over 6
RHS equals straight pi over 2
So comma space LHS not equal to RHS
Thus comma space straight x equals 1 half space is space not space straight a space solution space of space the space given space equation.
If space straight x equals 0 comma
LHS equals sin to the power of negative 1 end exponent left parenthesis 1 minus straight x right parenthesis minus 2 sin to the power of negative 1 end exponent straight x equals sin to the power of negative 1 end exponent open parentheses 1 close parentheses minus 2 sin to the power of negative 1 end exponent open parentheses 0 close parentheses equals straight pi over 2 minus 0 equals straight pi over 2
RHS space equals space straight pi over 2
So comma space LHS equals RHS
So comma space straight x equals 0 space is space straight a space solution space of space the space given space equation space. end style
Answered by Rebecca Fernandes | 28 Oct, 2016, 08:31: AM
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