How do you verify the identity ${cot}^{2} θ {csc}^{2} θ - {cot}^{2} θ = {cot}^{4} θ$ $cot^2thetacsc^2theta-cot^2theta=cot^4theta$ ?

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Answer 1 · 2016-08-24T18:01:02

See the Explanation.

Since, ${csc}^{2} θ = {cot}^{2} θ + 1$ $csc^2theta=cot^2theta+1$ , we have,

The L.H.S. $= {cot}^{2} θ ({cot}^{2} θ + 1) - {cot}^{2} θ$ $=cot^2theta(cot^2theta+1)-cot^2theta$

$= {cot}^{4} θ + {cot}^{2} θ - {cot}^{2} θ$ $=cot^4theta+cot^2theta-cot^2theta$

$= {cot}^{4} θ$ $=cot^4theta$

$= The R.H.S$ $="The R.H.S"$ .

How do you verify the identity cot^2thetacsc^2theta-cot^2theta=cot^4thetacot2θcsc2θ−cot2θ=cot4θcot^2thetacsc^2theta-cot^2theta=cot^4theta?