Solve 2csc2x=2sec2x?

2 Answers
Jun 25, 2018

x=π4±πn
x=3π4±πn

Explanation:

I assume you mean solve it

2csc2x=2sec2x

Set the expression equal to 0:
2csc2x2sec2x=0

Factor out the 2csc2x by dividing the left side of the equation by 2csc2x:

2csc2x(12sec2x2csc2x)=0

Apply reciprocal identities:

2csc2x11cos2x1sin2x=0

2csc2x(11cos2xsin2x)=0

2csc2x(1sin2xcos2x)=0

Apply quotient identity:
2csc2x(1tan2x)=0

Set factors equal to 0 and solve:
tan2x=1
tanx=±1
x=π4±πn
x=3π4±πn

cscx=0
No solution

Jun 26, 2018

x=±π4+kπ

Explanation:

csc2xsec2x=0
(cscxsecx)(cscx+secx)=0
(1sinx1cosx)(1sinx+1cosx)=0
(sinxcosx)(sinx+cosx)=0
a. sin x - cos x = 0
Divide both sides by cos x
(condition cosx0, or xπ2, or x3π2)
tan x = 1
Trig table and unit circle give -->
x=π4+kπ
b. sin x + cos x = 0 --> tan x = -1
x=π4+kπ
General answer: x=±π4+kπ