Evaluates :

$open vertical bar table row cell sin space 30 degree end cell cell space space cos space 30 degree end cell row cell negative sin space 60 degree end cell cell space cos space 60 degree end cell end table close vertical bar$

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Solution

Let space space increment space equals space open vertical bar table row cell sin space 30 degree end cell cell space space cos space 30 degree end cell row cell negative sin space 60 degree end cell cell space cos space 60 degree end cell end table close vertical bar space space space space space space space space space space space space equals space sin space 30 degree space cos space 60 degree space space plus space cos space 30 degree space space sin space 60 degree space equals space sin space left parenthesis 30 degree space plus 60 degree right parenthesis space space space space space space space space space space space space equals space sin space 90 degree space equals 1

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