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Inverse Trigonometric Functions

Question
CBSEENMA12032611
Wired Faculty App

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

Solution

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)  
                                          

Question
CBSEENMA12032612
Wired Faculty App

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

Solution

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

Question
CBSEENMA12032613
Wired Faculty App

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

Solution

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

Question
CBSEENMA12032614
Wired Faculty App

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

Solution

WiredFaculty 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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