Inverse Trigonometric Functions

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Question

Solve the following for x:

$sin to the power of negative 1 end exponent left parenthesis 1 minus straight x right parenthesis minus 2 sin to the power of negative 1 end exponent straight x equals straight pi over 2$

Solution

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 space equals space straight pi over 2 rightwards double arrow space space sin to the power of negative 1 end exponent left parenthesis 1 minus straight x right parenthesis space equals space straight pi over 2 plus 2 sin to the power of negative 1 end exponent straight x rightwards double arrow space space left parenthesis 1 minus straight x right parenthesis space equals space sin left parenthesis straight pi over 2 plus 2 sin to the power of negative 1 end exponent straight x right parenthesis space rightwards double arrow space space left parenthesis 1 minus straight x right parenthesis space equals space cos left parenthesis 2 sin to the power of negative 1 end exponent straight x right parenthesis space rightwards double arrow space space left parenthesis 1 minus straight x right parenthesis space equals space cos left parenthesis cos to the power of negative 1 end exponent left parenthesis 1 minus 2 straight x squared right parenthesis right parenthesis space rightwards double arrow space left parenthesis 1 minus straight x right parenthesis equals space left parenthesis 1 minus 2 straight x squared right parenthesis space rightwards double arrow space 1 minus straight x equals 1 minus 2 straight x squared space space rightwards double arrow 2 straight x squared minus straight x space equals space 0 therefore straight x space equals 0 comma space space straight x space equals space 1 half space space space space space

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Inverse Trigonometric Functions

Solve the following for x:

$sin to the power of negative 1 end exponent left parenthesis 1 minus straight x right parenthesis minus 2 sin to the power of negative 1 end exponent straight x equals straight pi over 2$

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