Thread: Simplifying expressions

1)Tan0 + Cot0

2)1-Sec(2)0
------------
1-Cosec(2)0

3) Sin0
----------
Cosec0 - Cot0

4) 1+Cos2 0


0 = 0 with a line through the middle, not sure how you do it on the forums, and anything in brackets is power of.

Any help with this would be appreciated.

thank you!

Originally Posted by Kim2425

1)Tan0 + Cot0

Let's call "0" = t for convenience.

tan(t) + cot(t) = sin(t)/cos(t) + cos(t)/sin(t) <-- Get a common denominator then add the fractions:

= [sin^2(t) + cos^2(t)]/[sin(t)cos(t)]

= 1/[sin(t)cos(t)]

We can work with this a bit more:

= 2/[2sin(t)cos(t)] = 2/sin(2t) = 2*csc(2t)

-Dan

TECHNICAL COMMENT: Tan(t) and tan(t) are technically two different functions. The correct usage for the common trig functions is sin(t), cos(t), tan(t), csc(t), sec(t), and cot(t).

Originally Posted by Kim2425

2)1-Sec^2(t)
------------
1-csc^2(t)

First note that:
1 - sec^2(t) = tan^2(t)
and
1 - csc^2(t) = cot^2(t)

So:
[1 - sec^2(t)]/[1 - csc^2(t)] = tan^2(t)/cot^2(t) = tan^4(t)

-Dan

Originally Posted by Kim2425

3) Sin(t)
----------
Csc(t) - Cot(t)

sin(t)/[csc(t) - cot(t)] = sin(t)/[1/sin(t) - cos(t)/sin(t)]

Multiply the numerator and denominator of the overall fraction by sin(t):

sin^2(t)/[1 - cos(t)] (We need to keep in the back of our minds that sin(t) cannot be 0 from here on, but it couldn't do that in the original expression anyway.)

Multiply the numerator and denominator by 1 + cos(t):

[sin^2(t)*(1 + cos(t))]/[1 - cos^2(t)] = [sin^2(t)*(1 + cos(t))]/[sin^2(t)]

= 1 + cos(t)

-Dan

Originally Posted by Kim2425

4) 1+Cos^2(t)

Is there a typo in here? I can't think of anything to do with this one.

-Dan