Precal help...proofs for trigonometric fuctions with factoring and multiplication?

Question

theres a worksheet that starts with proofs that involve factoring, the 1st two questions are:
1) sin^(2)x-sin^(2)xcos^(2)=sin^(4)x

2) sinxcos^(2)x-sinx= -sin^(3)x

The flip side says proofs that involve multiplication, and two questions on it are:
1) (secx+1)(sec s -1)= tan^(2)x

2) sinx (cscx-sinx)=cos^(2)x

could someone do these four so i have something to go off of or even better explain this? thanks!!

Answer 1

1) sin^2 - sin^2cos^2 = sin^2(1 - cos^2) = sin^2sin^2 = sin^4
2) sin cos^2 - sin = sin (cos^2 - 1) = -sin (1 - cos^2) = -sin (sin^2) = - sin^3

3) (sec + 1)(sec - 1) = (sec^2 - 1) = (1/cos^2 - 1) = (1 - cos^2)/cos^2 = sin^2/cos^2 = tan^2
4) sin (csc - sin) = sin (1/sin - sin) = 1 - sin^2 = cos^2

sin^2+cos^2 = 1, this is key.

Answer 2

I had a similar question and got help at http://www.schoolpiggyback.com ...its a bunch of students that help you out with the assignment...maybe someone from your class...lol...goodluck : )