Question

Prove: ((cot^2-1)/csc^2) = cos2

Answer 1

change into sin and cos

Answer 2

see
(cot^2 x - 1)/cosec^2x
=((cos^2 x/ sin^2 x) - 1) / cosec^2x
=( cos^2 x - sin^2 x)/sin^2 x ) / cosec^2x
= ( cos^2 x - sin^2 x)/(sin^2 x * cosec^2x)
=( cos^2 x - sin^2 x)
=cos2x

Answer 3

That was really, really, helpful! I didn't think of answer it in that manner. Thank you!

Answer 4

welcome dear

Answer 5

Last question, though! How did you get these:
= ( cos^2 x - sin^2 x)/sin^2 x ) / cosec^2x
= ( cos^2 x - sin^2 x)/(sin^2 x * cosec^2x)

For the first one, is this what you did: ((cos^2/sin^2)*(1 or sin^2/sin^2))/csc^2?
I'm trying to get it, but I can't figure out how you got the second one. :O

Answer 6

( (cos^2 x - sin^2 x)/sin^2 x ) / (cosec^2x /1)
= ( (cos^2 x - sin^2 x)/sin^2 x ) * (1/ cosec^2x)
= ( cos^2 x - sin^2 x)/(sin^2 x * cosec^2x)