Solve sec x / csc x - 1 = 0 for all real values of x.?

Answer 1

secx = 1/cosx

cscx = 1/sinx

sec x / csc x = (1/cosx)/(1/sinx) = sinx/cosx = tanx

So what you have is:

tanx - 1 = 0

==> tanx = 1

This is true for x at all integral values of 45 degrees (π/4 radians).

Answer 2

sec(x) / csc(x) - a million = 0 sec(x) / csc(x) = a million sec(x) = csc(x) a million/cos(x) = a million/sin(x) sin(x) = cos(x) tan(x) = a million x = pi/4 + pi * ok, ok is an integer except you meant: sec(x) / (csc(x) - a million) = 0 in which case, we only might want to discover at the same time as the numerator is 0 sec(x) = 0 a million / cos(x) = 0 a million = 0 by no skill occurs.

Answer 3

sec x = 1/cos x

and
csc x = 1/sen x

=>
sec x / csc x - 1 = 0
(1/cos x) / (1/sen x) - 1 = 0
sen x*(1/cos x) / (1 - sen x) = 0
tg x / (1 - sen x) = 0
(tg x+1-1) / (1 - sen x) = 0

(tg x+1) / (1 - sen x) = 1/(1 - sen x)
[tg x+1] = 1
tg x = 0
sen x / cos x = 0
sen x = 0

x = 90º

or
sec x / csc x - 1 = 0
(1/cos x) / (1/sen x) - 1 = 0
sen x*(1/cos x) / (1 - sen x) = 0
tg x / (1 - sen x) = 0
tg x = 0
sen x / cos x = 0
sen x = 0

x = 90º

=>
m = 180
(y-90)=180(x-0)
y = 180x+90

Answer: the numbers are 180x+90 degrees.

₢

Answer 4

Not quite. In the unit circle the solutions are pi/4 and 5pi/4 (third quadrant). So the geenral solution is x = n*pi + pi/4.

Answer 5

secx=1/cosx
cosecx=1/sinx
secx/cscx=1/cosx/1/sinx
=sinx/cosx
=tanx
the equation
tanx-1=0
tanx=1
tanx=tanpi/4
x=npi+pi/4
where n is element of integers

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