Thread: Proving Identities

I am still having problems on this proving identity problem:

tan^2t/sect = sect - cost

If someone could please help me I would greatly appreciate it.

There.
Only one. And clear.

tan^2t/sect = sect - cost

tan^2(T)/secT = secT -cosT
We develop the Lefthand Side (LHS) while the RHS stays.
Convert the tan and sec into sin and/or cos,
LHS = tan^2(T)/secT
= [(sinT / cosT)^2] / [1 / cosT]
= [sin^2(T) / cos^2(T)]*[cosT / 1]
= sin^2(T) / cosT
Since sin^2(T) +cos^2(T) = 1, then,
= [1 -cos^2(T)] / cosT
= 1/cosT -cos^2(T)/cosT
= secT -cosT
And that is the same as the RHS.
Therefore, proven.

we have

Tan^2t=sec^2t - 1

so
Tan^2t/sect=(sec^2t - 1 )/sect

that gives the right hand side as sect - cost