Question

Math Analysis: Simplify each expression.
(cot^2 x/1 + csc x) + sin x*csc x

Answer 1

((Cos^2/Sin^2) + (1/Sin)) + Sin*(1/Sin)
uhmm typing out cos and sin is annoying, ill use a for sin and b for cos

Answer 2

can we use a for cos and b for sin? :D

Answer 3

sure.. hold on

Answer 4

((a^2/b^2) + (1/b)) + b*(1/b) = ( (a^2/b^2) + (b/b^2) ) + 1
= (a^2+b)/b^2 + 1

Answer 5

(Cos^2 + Sin)/Sin^2 + 1

Answer 6

where did you get +1/b from?

Answer 7

csc = 1/sin

Answer 8

idk if that can be simplified further. We'll probably end up going around in circles.

Answer 9

ok so were left with (cos^2 + sin/ sin^2) + 1 so how'd you get csc?

Answer 10

it was in your question.

Answer 11

the answer was csc btw at the back of the book but I want to know how you get that

Answer 12

how would i get that answer im still confused

Answer 13

sinx*cscx would cancel out of the equation so were left with (cot^2/1 +csc) + 1

Answer 14

let me do this on paper, im getting confused typing.

Answer 15

okay lol

Answer 16

Here you go:
\[(Cot^2x)/(1+Cscx)+Sinx*Cscx=\]
\[(Cos^2x/Sin^2x)/(1+(1/Sinx))+Sinx*(1/Sinx)=\]
\[(Cos^2x/Sin^2x)/(1+(1/Sinx))+1=\]
\[(Cos^2x/Sin^2x)/((Sinx+1)/Sinx))+1=\]
\[(Cos^2x/Sin^2x)*(Sinx/(Sin+1))+1=\]
\[Cos^2x/(Sin^2x+Sinx)+1=\]
\[(1-Sin^2x)/(Sin^2x+Sinx)+1=\]
\[(1-Sinx)(1+Sinx)/(Sinx(1+Sinx))+1=\]
\[(1-Sinx)/Sinx + 1=\]
\[(1/Sinx)-(Sinx/Sinx)+1=\]
\[(1/Sinx)-1+1=\]
\[(1/Sinx)+0=1/Sinx=Cscx\]

Answer 17

beautiful answer, isn't it :). Pain to type though.

Answer 18

Still digesting? lol

Answer 19

yeah its really long o-o

Answer 20

i dont get (cos^x/sin^2x)*(sinx/sinx + 1) +1 = (cos^2x/sin^2x + sinx) +1
shouldn't it = (cos^2x/sin^2x+1) + 1?

Answer 21

Where? which line?

Answer 22

6th line

Answer 23

Write it out on a piece of paper, you'll see it immediately. I cancelled out Sin on top with Sin^2 on bottom, that left me with a Sin on the bottom which I distributed into the second fractions denominator.

Answer 24

but where did the 1 on the bottom go?

Answer 25

so the 1 became a sinx?

Answer 26

Yes, can't u see i have them under a common denominator? Pay attention to the parenthesis, they are important.

Answer 27

i still cant understand can you explain how the 1 turned into a sin x I get the rest its just that part. :\