Trig Proofs

[johnjohn320]

Hey all,

I'm fine with all of this stuff except for two proofs that are stumping me for some reason. Can you give me a hand?

1/(1+cosx) + 1/(1-cosx) = 2csc^2 (x)



AND



(1-sec(x)) / (1+sec(x)) = (cos(x)-1) / (cos(x)+1)

 

[PrincessGuard]

1st one is easy. Find a common denominator and use sin^2+cos^2=1.

 

[MrSmithers]

2nd one, write sec as cos and it is a simple common denominator/division from there.

 

[aux]

For the first one use:
2*(sin(x/2))^2 = 1-cos(x)
2*(cos(x/2))^2 = 1+cos(x)
substitute the above in 1/(1+cosx) + 1/(1-cosx), after common denominator,
the nominator will be (sin(x/2))^2 + (cos(x/2))^2 = 1
the denominator will be 2*[(sin(x/2))^2]*[(cos(x/2))^2], which is 0.5*[sin(x)^2] (because 2*sin(x/2)*cos(x/2) = sin(x))