# Appreciated help.

• Nov 27th 2009, 10:35 AM
Silvahere
Appreciated help.
There are a few questions that my teacher did not make clear when explaining our lesson. Can you guys explain?

1. How could these be simplified?
a. 1+tan² theta / 1+cot theta

I already know that it simplifies to:
sec² theta / csc² theta
What else could be done?

b. sect+csct / 1+tant

c. sin(x+y)cosy - cos(x+y)siny

d. 2sin2asin2a

e. Square root of: 1+cos2beta / 2 (end square root)
Restrictions: -pi/2 < beta < pi/2

f. Dear god this is a hard one.
tan7pi/6 - tanpi/3 all over 1 + tan7pi/6 tanpi / 3

I promise, you guys aren't doing my homework. :P I just have a bad teacher.

2. Solve the trig functions within [0, 2pi)
a. cos3x + cosx = 0

b. cot²x + cos²x = cot²xcos²x

3. Stupid proofs... Prove the identities. T__T'
a. cscx/cscx-1 + cscx/cscx+1 = 2sec²x

b. sinasinbeta(cotacotbeta-1) = cos(a+beta)

c. cos^4y - sin^4y = cos2y

d. tan(pi/4 + p)

4. Find the values (w/out calculator)
a. cos[cos^-1(-1/2) + sin^-1 1]

b. tan[cos^-1 (-1)-cos^-1 1]

5. :/ Find exact values of sin2u and cos u/2.

a. cscu = 2
Restriction: pi/2 < u < pi

b. tanu = -8/5
Restriction: 3pi/2 < u < 2pi

I'm soo sorry. I feel like I'm asking way too much. x___x'
• Nov 27th 2009, 12:07 PM
mr fantastic
Please don't post more than two questions in a thread. Otherwise the thread can get convoluted and difficult to follow. Start new threads as necessary for remaining questions. eg. If you have five questions, post three of them in one thread and start a new thread for the remaining two etc.

And if the question has more than two parts to it, it is best to post only that question and its parts in the thread and start a new thread for other questions.