Question

Solve tan2A - 2tanA = -1 for 0º≤A≤360º.

Answer 1

tan^2A - 2tanA = -1*

Answer 2

\[\frac{ 2\tan A }{1-\tan ^{2}A }-2\tan A=-1\]
\[2\tan A \left( \frac{ 1 }{1-\tan ^{2}A }-1 \right)=-1\]
\[2\tan A \left( \tan ^{2}A \right)=-1+\tan ^{2}A\]
\[2\tan ^{3}A=\sec ^{2}A\]
R.H.S is positive ,hence L.H.S. is also positive
So A lies in ist or 3rd quadrant.

Answer 3

Would the answer be 45 degrees and 225 degrees or 60 and 240?

Answer 4

since both are in the same quadrants...

Answer 5

\[now you have mentioned \it is \tan ^{2}A\]

Answer 6

yes I'm sorry!

Answer 7

\[\tan ^{2}A-2 \tan A=-1or \tan ^{2}A-2\tan A+1=0\]
\[\left( \tan A-1 \right)^{2}=0,\tan A=1,A=45,225\]

Answer 8

Thank you for your assistance!

Answer 9

yw