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]#