Evaluates : from Mathematics Inverse Trigonometric Functions Cl
Evaluates :
open vertical bar table row cell sin space 30 degree end cell cell cos space 30 degree end cell row cell negative sin space 60 degree end cell cell cos space 60 degree end cell end table close vertical bar

Let space increment space equals space open vertical bar table row cell sin space 30 degree end cell cell cos space 30 degree end cell row cell negative sin space 60 degree end cell cell cos space 60 degree end cell end table close vertical bar
space space space space space space space space space equals space sin space 30 degree space cos space 60 degree space plus cos space 30 degree space sin space 60 degree space equals sin space left parenthesis 30 degree space plus space 60 degree right parenthesis
space space space space space space space space space equals space sin space 90 degree space equals space 1
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Evaluate
open vertical bar table row cell 2 space space space space space 4 end cell row cell negative 1 space space space space 2 end cell end table close vertical bar

Let    increment space equals space open vertical bar table row cell 2 space space space space space 4 end cell row cell negative 1 space space space space 2 end cell end table close vertical bar = (2) (2) - (4) (- 1) = 4 + 4 = 8

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Evaluate  open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar


 increment equals open vertical bar table row straight x cell straight x plus 1 end cell row cell straight x minus 1 end cell straight x end table close vertical bar
=(x) (x) - (x + 1) (x - 1) (x - 1) = x2 - (x2 - 1) = x2 - x2 + 1 = 1
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Evaluate  open vertical bar table row 2 cell space space 4 end cell row cell negative 5 end cell cell negative 1 end cell end table close vertical bar


Let increment equals open vertical bar table row cell space space space 2 end cell cell space space 4 end cell row cell negative 5 end cell cell negative 1 end cell end table close vertical bar=(2) (- 1) - (4) (- 5) =  - 2 + 20 = 18

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Evaluates :
open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar


Consider open vertical bar table row cell straight a plus ib space space space space space straight c plus id end cell row cell negative straight c plus id space space space space space straight a minus ib space space space end cell end table close vertical bar = (a + i b) (a - i b)-(c + i b)(- c + i d)
                                            = (a2 - i2 b2 ) - (i2 d2 - c2)
                                            = (a2 + b2 ) - (- d2 - c2)                        [ because i2 = - 1 ]
                                            = (a2 + b2 + c2 + d2)  
                                          

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