Question

Question #4fec2

Answer 1

If you have:
`(cot^2(x)+1)*(1-cos^2(x))` (I)

You can write:
`cot^2(x)=cos^2(x)/sin^2(x)` and from:
`sin^2(x)+cos^2(x)=1` (II)
you get:
`sin^2(x)=1-cos^2(x)`
substituting in (I):
`(cos^2(x)/sin^2(x)+1)*sin^2(x)=` multiplying:
`=(cos^2(x)*sin^2(x)/sin^2(x)+sin^2(x))=` the same as (II)
`=cos^2(x)+sin^2(x)`
Which is equal to `1` for every angle `x`
(Try to substitute values of `x` in the above expression to check)

Hope it helps