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?
No idea about the rest...
b. sect+csct / 1+tant
c. sin(x+y)cosy - cos(x+y)siny
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'