CPhill

Good job, Heather  !!!    (LOL !!!)

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1 / [ 1 + sinΘ]  + 1 / [1 - sinΘ]  getiing a common denominator, we have

[1 - sinΘ + 1 + sinΘ ] / [ 1 - sin²Θ]  =

2/[1- sin²Θ] =

2/cos²Θ  =

2sec²Θ

If cot(x)  = 5, we have  x/y  = 5/1

So 

r = √[5^2 + 1^2] = √[25 + 1 ] = √26

And csc(x) = r / y = √26  / 1   =  √26

No, Heather....re-read.....

f(t-1)  = (t-1)^3 + 6(t-1)^2 + 12(t-1) + 8  =

[t^3 - 3t^2 + 3t - 1] + [6t^2 - 12t + 6] + [12t - 12 ] + 8 =

t^3 + 3t^2  + 3t + 1     =  (t + 1)^3

So...the coefficients  are  (1,3,3,1 )

cosΘ - tanΘ   =0     add tanΘ  to both sides

cosΘ  = tanΘ

The easiest way to solve this - IMHO - is with a graph.......here it is....

7x+5z=4+8y   subtract 4 from both sides

7x + 5z - 4  = 8y      divide both sides by 8

[7x + 5x - 4] / 8  = y

I think this is supposed to be :

cotΘtanΘ  =

[cosΘ / sinΘ ] [sinΘ / cosΘ]=

1