help on a dificult proof?

Question

cot^2- cos^2 = (cot^2)(cos^2)

Answer 1

cot^2 - cos^2
= (cos^2)/(sin^2) - cos^2
=(cos^2 - cos^2sin^2)/sin^2
=(cos^2(1-sin^2)/sin^2
=cos^2 cos^2/sin^2
=cot^2cos^2 = RHS

Answer 2

cot^2 - cos^2 = (cot^2)(cos^2) turn to sin's and cos's

(cos^2)/(sin^2) - cos^2 = (cos^2)/(sin^2) * (cos^2) common demoninator

(cos^2)/(sin^2) - (sin^2*cos^2)/(sin^2) = (cos^4)/(sin^2) subtract and multiply by sin^2

cos^2 - (sin^2cos^2) = cos^4 factor out cos^2 and divide

1 - sin^2 = cos^2 use (sin^2 + cos ^2 = 1) and substitute

cos^2 = cos^2

Answer 3

cot^2 theta - cos^2 theta = (cot^2 theta )(cos^2 theta), best to write in terms of sin/cos

cos^2 theta/ sin^2 theta - cos^2 theta = (cos^2 theta/ sin^2 theta)* cos^2 theta, combine left side

(cos^2 theta - cos^2 theta sin^2 theta)/ sin^2 theta = cos^2 theta* cos^2 theta/ sin^2 theta, factor out cos^2 theta

cos^2 theta (1 - sin^2 theta)/ sin^2 theta = cos^2 theta*cos^2 theta/sni^2 theta, use Phyth ID

cos^2 theta * cos^2 theta/ sin^2 theta = cos^2 theta* cos^2 theta/sin^2 theta, done.

Please note, you were missing the ANGLE when you wrote it down!