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Simplify sec^2x-tan x-3

Sagot :

Sec^2x-tan x-3 = RED IS SUS

[tex]\huge\longmapsto\mathfrak{Answer}[/tex]

=》

[tex] \sec {}^{2} (x) - tan(x) - 3[/tex]

=》

[tex] \tan {}^{2} (x) + 1 - \tan(x) - 3[/tex]

=》

[tex] \tan {}^{2} (x) - \tan(x) - 2[/tex]

=》

[tex] \tan {}^{2} (x) - 2\tan(x) + \tan(x) - 2[/tex]

=》

[tex] \tan(x) ( \tan(x) - 2) + 1( \tan(x) - 2) [/tex]

=》

[tex]( \tan(x) + 1)( \tan(x) - 2)[/tex]

so,

case - 1

=》

[tex] \tan(x) = - 1[/tex]

case - 2

[tex] \tan(x) = 2[/tex]