Question

2tanx - (1+tanx)^2 = -sec^2

Answer 1

how can i change the left hand into -sec^2?

\[2\tan \Theta -(1+ \tan \Theta)^{2}\]

Answer 2

\[\large \bf 2tanx-(1+tanx)^2\]
open the bracket first,
\[\large \bf 2tanx-(1+\tan^2x+2tanx)\]
\[\large \bf 2tanx-1-\tan^2x-2tanx\]
+2tanx and -2tanx cancel out,
we get
\[\large \bf -1-\tan^2x=-(1+\tan^2x)\]
we know that,
\[\large \bf 1+\tan^2x=\sec^2x\]
finally,we get
\[\large \bf -\sec^2x=\color{red}{Right~hand~side}\]
\[\huge \bf \color{green}{Hence~Proved}\]

Answer 3

hope you understand. @zubhanwc3

Answer 4

ah, wow i made a simple algebra mistake, i made (1-tan)^2 1-tan^2 >.> tyvm

Answer 5

welcome :)