Question

Solve equation: tan^2x-2secx
give possible solutions

Answer 1

what's the equation?

Answer 2

\[\tan ^{2}\theta-2\sec \theta=2\]

Answer 3

\(\large tan^2\theta-2sec\theta=2 \)
\(\large tan^2\theta-2sec\theta-2=0 \)
\(\large [tan^2\theta-2sec\theta-2=0]\cdot cos^2\theta \)
\(\large sin^2\theta-2cos\theta-2cos^2\theta=0 \)
\(\large sin^2\theta-2cos\theta-2(1-sin^2\theta)=0 \)
\(\large sin^2\theta-2cos\theta-2+2sin^2\theta=0 \)
\(\large 3sin^2\theta-2cos\theta-2=0 \)

can you take it from here? it's now a trig equation in quadratic form...

Answer 4

why did you multiply everything but cos^2theta

Answer 5

I think you'd be better off making the sub.s tan^2 = sec^2-1

Answer 6

you get
sec^2 x -2sec x -3 =0
(sec x -3)(sec x+1) =0

Answer 7

okay, i set everything to 0?

Answer 8

sorry... in the third line i should've changed the sin^2 to cos^2:
\(\large sin^2\theta-2cos\theta-2cos^2\theta=0 \)
\(\large (1-cos^2\theta)-2cos\theta-2cos^2\theta=0 \)
\(\large 1-2cos\theta-3cos^2\theta=0 \)
\(\large 3cos^2\theta+2cos\theta-1=0 \)

that's better....

Answer 9

*4th line, not 3rd line

Answer 10

okay that makes more sense now