Solve the equation $2sec^2theta+3tantheta=1$ ?

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Answer 1 · 2017-06-12T16:34:25

$theta=2.678$ or $2.3562$ radians

As $sec^2theta=1+tan^2theta$

$2sec^2theta+3tantheta=1$ can be written as

$2+2tan^2theta+3tantheta=1$

or $2tan^theta+3tantheta+1=0$

i.e. $(2tantheta+1)(tantheta+1)=0$

Hence either $tantheta=-1/2=tan(pi-0.4636)=tan2.678$ (in radians)

or $tantheta=-1=tan((3pi)/4)=tan2.3562$ (in radians)

These are results in $[0,pi]$

Solve the equation 2sec^2theta+3tantheta=12sec^2theta+3tantheta=1?