Question

How do you simplify `tan t * cot t - sin^2 t`?

Answer 1

`cos^2t`

Explanation:

`tan tcot t= tan tx (1/tan t)=1`
`1-sin^2t=(sin^2 t+cos^2 t)-sin^2 t=cos^2t`

Answer 2

This problem requires some trigonometric identities,here,
1) cotx=1/tanx
2)`sin^2x`+`cos^2x`=1 or `cos^2x`=1-`sin^2x`

Explanation:

1) tan t*cot t -`sin^2t`* = tan t 1/tan t-`sin^2t`........(putting identity .1)
= 1-`sin^2t`................(putting identity .2)
= `cos^2t`
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I hope this helps :)