How do you verify ${csc}^{4} - 2 {csc}^{2} x + 1 = {cot}^{4} x$ $csc ^4 -2csc ^2 x +1 = cot^4 x$ ?

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How do you verify ${csc}^{4} - 2 {csc}^{2} x + 1 = {cot}^{4} x$ $csc ^4 -2csc ^2 x +1 = cot^4 x$ ?

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Answer 1 · 2015-08-12T13:00:05

${sin}^{2} A + {cos}^{2} A = 1$ $sin^2 A + cos^2 A = 1$
Divide by sin^2 A:
$1 + {cot}^{2} A = {csc}^{2} A$ $1 + cot^2 A = csc^2 A$

${csc}^{4} x - 2 {csc}^{2} x + 1 = {({csc}^{2} x - 1)}^{2} = {({cot}^{2} x)}^{2} = {cot}^{4} x$ $csc^4 x - 2csc^2 x + 1 = (csc^2 x - 1)^2 = (cot^2 x)^2 = cot^4 x$

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How do you verify ${csc}^{4} - 2 {csc}^{2} x + 1 = {cot}^{4} x$ $csc ^4 -2csc ^2 x +1 = cot^4 x$ ?

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How do you verify csc4−2csc2x+1=cot4xcsc ^4 -2csc ^2 x +1 = cot^4 x?

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How do you verify ${csc}^{4} - 2 {csc}^{2} x + 1 = {cot}^{4} x$ $csc ^4 -2csc ^2 x +1 = cot^4 x$ ?