Maths homework (yes, I know!)

[UK31337]

I know I shouldn't be asking.

Gah, Maths is so pointless, but I'm stuck with it until January. Can anybody help me out?

I've got to Show that:

a) (1-cos²t)(1+cotan²t)=1

b) tanθ + cotanθ = 1/ cosθsinθ

c) sinθtanθ+cosθ = secant θ

I don't need to solve the equations or find any values, I've just got to show the statements are true. I don't know where to start with these three buggers.

Anybody? Pointless trig is my main sticking point. Any ideas?

 

[mammikoura]

well u can prove them right by calculating them.
Sin, Cos and Tan are angles, u need to have a calculator which knows these. If u don't u can use the one on windows.

Other than that it goes beyond my understanding.

 

[catalyst1]

a)
(1-cos²t)(1+cotan²t)=1
(1-(1-sin²t))(1+(csc²t-1))=1
(sin²t)(csc²t)=1
sin²t(1/sin²t)=1
1=1

b)
tan(t) + cotan(t) = 1/(cos(t)sin(t))
sin(t)/cos(t) + cos(t)/sin(t) = 1/(cos(t)sin(t))
sin²(t)/(sin(t)cos(t)) + cos²(t)/(sin(t)cos(t)) = 1/(cos(t)sin(t))
(sin²(t) + cos²(t))/(sin(t)cos(t)) = 1/(cos(t)sin(t))
1/(sin(t)cos(t)) = 1/(cos(t)sin(t))

c)
sin(t)tan(t) + cos(t) = sec(t)
sin(t)(sin(t)/cos(t)) + cos(t) = sec(t)
sin²(t)/cos(t) +cos²(t)/cos(t) = sec(t)
(sin²(t) + cos²(t))/cos(t) = sec(t)
1/cos(t) = sec(t)
sec(t) = sec(t)

 

[catalyst1]

please delete this post

 

[lhuser]

sooo much to do...>_<

 

[catalyst1]

It's not too hard as long as you know your trig identities.