Question

Solve the following equation, giving the exact solutions which lie in [0, 2π). (Enter your answers as a comma-separated list.)

tan^2(x)=3/2sec(x)

Answer 1

can u plz rewrite ur question more explicitly...

Answer 2

\[\tan ^{2}(x)=\frac{ 3 }{ 2 }\sec(x)\]

Answer 3

what do you mean?

Answer 4

Change them into \(\sin\) and \(\cos\).

Answer 5

now its bit more clear

Answer 6

thus we have
sin^2(x)/cos^2(x) =(3/2cosx)
or (1 - cos^2(x))/cos^2(x) =3/(2cosx) ...
i think now it can be solved after cross multiplication)

Answer 7

matri could you go on? Im kinda clueless

Answer 8

where do you find the prob in the above expression

Answer 9

how do i cross multiply that?

Answer 10

as u usually do it for regular equation

Answer 11

2cosx *((1 - cos^2(x)) = 3 cos^2(x) .....

Answer 12

2cosx *(1 - cos^2(x)) - 3 cos^2(x) =0
or cosx*(2(1 - cos^2(x)) -3cosx)=0......
cosx*(2(1 - cos^2(x) )-3cosx) =0
cosx*(2 - 2cos^2(x) -3cosx)=0
cosx*(2 -4cosx +cosx -2cos^2(x) )=0
cosx * (2*(1-2cosx) +cosx(1-2cosx))=0
or
cosx *(2+cosx)*(1-2cosx)=0
hence cosx = 0 or cosx =1/2 [as cosx <>-2]

Answer 13

i hope further u can do it...