How do you simplify the expression $tan^2t(csc^2t-1)$ ?

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Answer 1 · 2017-01-20T13:37:54

$1.$

We use the Identity $csc^2t=1=cot^2t$ to get,

$tan^2t(csc^2t-1)=(tan^2t)(cot^2t)=1$ .

Otherwise , substituting $sint/cost" for "tant" and "1/sint" for "csct$ ,

The L.H.S. $=(sin^2t/cos^2t){1/sin^2t-1}$

$={cancel(sin^2t)(1-sin^2t)}/{(cos^2t)cancel(sin^2t)}$

$=cos^2t/cos^2t$

$=1.$

How do you simplify the expression tan^2t(csc^2t-1)tan^2t(csc^2t-1)?