Question

solve 2 sec^2 x + tan^2 x - 3=0

Answer 1

we have
\[2 \sec^2 x+\tan ^2 x-3=0\]
@Busterkitten what's the relation between tan^2 x and sec^2 x?

Answer 2

Okay we have the relation as
\[\tan^2 x+1=\sec^2x\]
Remember it always it's an important relation:)

Answer 3

We are given
\[2sec^2x+tan^2x-3=0\]
substitute
\[tan^2 x=sec^2 x-1\]
\[2 \sec^2 x+ \sec^2 x-1-3=0\]
we get
\[3 \sec^2x-4=0\]
or
\[\sec^2x= \frac{4}{3}\]
we get
\[\sec x= \pm \frac{2}{\sqrt 3}\]
now when
\[\sec x= \frac{2}{\sqrt 3}\]
x= 30 degrees
when
\[\sec x= -\frac{2}{\sqrt 3}\]
x= 360-30=330
so x is either 30 or 330 degrees

Answer 4

wouldn't be also be 210 and 150 cause the radical made the the # - and +

Answer 5

Yeah you are right. Missed them . Sorry:(

Answer 6

kk I can understand and thank you