How do you simplify $1+cot^2theta-cos^2theta-cos^2thetacot^2theta$ ?

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Answer 1 · 2017-02-04T15:35:55

$1$

$=1 + cot^2theta - cos^2theta(1 + cot^2theta)$

We can now simplify using $1 + cot^2alpha = csc^2alpha$ .

$= csc^2theta - cos^2theta(csc^2theta)$

$=csc^2theta - cos^2theta(1/sin^2theta)$

Use $cosalpha/sinalpha = cotalpha$ :

$=csc^2theta - cot^2theta$

Rearrange the above identity to get $1 = csc^2alpha - cot^2alpha$

$=1$

Hopefully this helps!

How do you simplify 1+cot^2theta-cos^2theta-cos^2thetacot^2theta1+cot^2theta-cos^2theta-cos^2thetacot^2theta?