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Principle Of Mathematical Induction

Question
CBSEENMA11013493
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Find the general solution of:

sec squared 2 straight x space equals space 1 minus tan 2 straight x




Solution
WiredFaculty                       rightwards double arrow       1 plus tan squared 2 straight x space equals space 1 minus tan 2 straight x

rightwards double arrow   tan squared 2 straight x plus tan 2 straight x space equals space 0                  rightwards double arrow          tan space 2 straight x left parenthesis tan space 2 straight x space plus space 1 right parenthesis space equals space 0

rightwards double arrow either      tan space 2 straight x space equals space 0                    or           WiredFaculty

rightwards double arrow either              2 straight x space equals space nπ comma space space straight n element of straight Z      or           tan space 2 straight x space equals space tan open parentheses negative straight pi over 4 close parentheses

rightwards double arrow either               straight x space equals space nπ over 2 comma space straight n space element of space straight Z    or         space space space 2 straight x space equals space nπ space minus space straight pi over 4 comma space straight n space element of space straight Z   
rightwards double arrow                        straight x space equals space nπ over 2             or             space space straight x space equals space nπ over 2 space minus space straight pi over 8 comma space straight n space element of space straight Z

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