Question

Simplify the expression 1 + cot²θ - cos²θ - cos²θ cot²θ ??

Answer 1

1

Explanation:

`1 + cot²θ - cos²θ - cos²θ cot²θ=`

`csc^2θ - cos²θ - cos²θ cot²θ=`

`csc^2θ - cos²θ (1+cot²θ)=`

`csc^2θ - cos²θ (csc^2θ)=`

`csc^2θ - cot²θ=`

`(1+cot^2θ) - cot²θ=`

`1`

Answer 2

Please see below.

Explanation:

A shorter way could be

`1+cot^2theta-cos^2theta- cos^2thetacot^2theta`

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

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

= `sin^2thetacsc^2theta`

= `1`