SOLUTION: trying to help my son but it has been 30 years for me doing these. {{{csc^4x - 2csc^2x + 1 = cot^4x}}} {{{(csc^2x)/(cot(x)) = csc(x)*sec(x)}}}

Algebra ->  Trigonometry-basics -> SOLUTION: trying to help my son but it has been 30 years for me doing these. {{{csc^4x - 2csc^2x + 1 = cot^4x}}} {{{(csc^2x)/(cot(x)) = csc(x)*sec(x)}}}       Log On


   

Question 271498: trying to help my son but it has been 30 years for me doing these.
csc%5E4x+-+2csc%5E2x+%2B+1+=+cot%5E4x


%28csc%5E2x%29%2F%28cot%28x%29%29++=++csc%28x%29%2Asec%28x%29
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

csc%5E4x+-+2csc%5E2x+%2B+1+=+cot%5E4x

Work with the left side only:

Factor the left side:

%28csc%5E2x-1%29%28csc%5E2-1%29=%22%22

Use the identity 1%2Bcot%5E2alpha=csc%5E2alpha or cot%5E2alpha=csc%5E2alpha-1

%28cot%5E2x%29%28cot%5E2x%29=%22%22

cot%5E4x=%22%22

--------------------------------------

%28csc%5E2x%29%2F%28cot%28x%29%29++=++csc%28x%29%2Asec%28x%29

Work with the left side only 

%28csc%5E2x%29%2F%28cot%28x%29%29=%22%22

Use the identity csc%28alpha%29=1%2F%28sin%28alpha%29%29 to
rewrite the numerator and the identity cot%28alpha%29=%28Cos%28alpha%29%29%2F%28Sin%28alpha%29%29 to rewrite the denominator:





Write as a division:

%0D%0A%0D%0A%28++1%2F%28Sin%5E2x%29+%29%22%F7%22++%28++%28Cos%28x%29%29+%2F%28Sin%28x%29%29++%29=%22%22

Invert the second fraction and change the division to multiplication:



Cancel



+%281%2F%28Sin%28x%29%29%29%281%2F%28Cos%28x%29%29%29=%22%22

Use the identities csc%28alpha%29=1%2FSin%28alpha%29 and sec%28alpha%29=1%2FCos%28alpha%29
to rewrite those factors

csc%28x%29sec%28x%29=%22%22

Edwin