Help with trig identities

[chargingkoala]

Hey, I've always had a lot of trouble with these.

I've got these two problems on my homework I've been working on for about 40 minutes together now and I've gotten nowhere.

They both want you to prove that the given equation is an identity.


The first:

1/(1+ sec s) + 1/(1 - sec s) = -2 cot² s



The second:

(1 + tan s)/(1 - tan s) = (sec² s + 2 tan s)/(2 - sec² s)


I need help with this start to finish.
Please and thank you.

 

[Deleted member 4993]

Hey, I've always had a lot of trouble with these.

I've got these two problems on my homework I've been working on for about 40 minutes together now and I've gotten nowhere.

They both want you to prove that the given equation is an identity.


The first:

1/(1+ sec s) + 1/(1 - sec s) = -2 cot² s

Treat the problem as regular addition of fraction - i.e. -

Start from the left-hand-side (LHS) of the equation,

find the Lowest Common Denominator (LCD),

make the denominators equal (to the LCD),

add and

use common trig identities.

The second:

(1 + tan s)/(1 - tan s) = (sec² s + 2 tan s)/(2 - sec² s)

Start with RHS

Use sec²(s) = 1 + tan²(s)

Factorize numerator and denominator - and

eliminate common factors from numerator and denominator - and

you are done.

I need help with this start to finish.
Please and thank you.

Please share your work with us, indicating exactly where you are stuck - so that we may know where to begin to help you.