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\(csc^4x-2csc^2x+1=cot^4x\)

zxElementzx  Dec 11, 2017
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csc^4x-2csc^2x+1=cot^4x

 

LHS=

\(LHS=cosec^4x-2cosec^2x+1\\ LHS=(cosec^2x-1)^2\\ LHS=\left(\frac{1-sin^2x}{sin^2x}\right)^2\\ LHS=\left(\frac{cos^2x}{sin^2x}\right)^2\\ LHS=\left(cot^2x\right)^2\\ LHS=cot^4x\\~\\ LHS=RHS \qquad QED\)

Melody  Dec 11, 2017

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