Question

WILL MEDAL & FAN!!

Using trigonometric identities solve 2Sec^2(x) = 5tan(x)-1

STEP BY STEP PLEASE

Answer 1

is it \[2 \sec ^2x\]?

Answer 2

yes!!

Answer 3

\[2\left( 1+\tan ^2x \right)=5\tan x-1\]
\[2 \tan ^2x-5 \tan x+2+1=0\]
\[2\tan ^2x-5\tan x+3=0\]
make factors and solve for tan x

Answer 4

@surjithayer thanks! how do i make factors?

Answer 5

@surjithayer ive been told by my tutor that tanx=0.5

Answer 6

\[2\tan ^2x-2\tan x-3\tan x+3=0\]

Answer 7

\[2 \tan x \left( \tan x-1 \right)-3\left( \tan x-1 \right)=0\]
\[\left( \tan x-1 \right)\left( 2\tan x-3 \right)=0\]

Answer 8

\[either~\tan x-1=0,\tan x=1,x=n \pi+\frac{ \pi }{ 4 },~where~n~is~an~integer.\]

Answer 9

\[or 2\tan x-3=0,2 \tan x=3,\tan x=\frac{ 3 }{ 2 },x=\tan^{-1} \left( \frac{ 3 }{ 2 } \right)\]

Answer 10

awesome thank you! @surjithayer

Answer 11

yw