i need help on my pre cal homework.?

Question

we're proving identities and i can not figure these two out.
1. 2-csc^2z = 1- cot^2z

2. (cot^3t)/(csct) = cost (csc^2t-1)

Answer 1

2 - csc²z =
2 - (1/sin²z) =
(2sin²z - 1) / sin²z =
(sin²z + sin²z - 1 ) / sin²z =
(sin²z - cos²z) / sin²z = {using trig id sin²+cos²=1}
1 - (cos²z / sin²z) =
1 - cot²z

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cot³t / csct =
(cos³t/sin³t) / (1/sint) =
(cos³t/sin³t) * sint =
cos³t/sin²t =
cost (cos²t/sin²t) =
cost (cot²t) =
cost (csc² -1) {using trig id 1+cot²=csc²}

Hope that helped!

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Answer 2

1.

2-csc²z = 1-cot²z
* Add csc² and cot² to both sides, and break 2 into 1 + 1
1 + (1 + cot²z) = (1 + csc²z)
* Substitute 1+cot² = csc²
1 + csc²z = 1 + csc²z
1=1

2.

cot³t/csct = cost(csc²t-1)
* Substitute csc² - 1 = cot²
cot³t/csct = cost(cot²t)
* Split off a cot, convert to cos/sin
cost/sint * cot²t/csct= cost(cot²t)
* Convert 1/csct to 1/1/sint = sint
cost/sint * cot²t * sint = cost(cot²t)
* Cancel sint
cost(cot²t) = cost(cot²t)
1=1

Answer 3

If cot(theta) is undefined, that probable skill the theta = 0, pi,..,n*pi. interior your constraints, theta could be pi, when you consider that 0 < pi/2, and 2*pi > 3*pi/2. the relax purposes are: sin(pi) = 0, cos(pi) = -a million, tan(pi) = 0 cosec(pi) = undef, sec(pi) = -a million i don't be attentive to what you propose by utilising x,y; and an perspective of pi (one hundred eighty deg) would not type a triange, yet lies on the damaging x-axis between quadrants IIi and IV