Question

I was given 21 questions for homework and I can't get the last few no matter how hard and how many times I try.

17. Sinx-1/sinx+1 = -cos^2x/(sinx+1)^2

18. Sin^4x + 2sin^2xcos^2x + cos^4x = 1

19. 4/cos^2x - 5 = 4tan^2x - 1

20. Cosx - sinx - cos^3x/Cosx = sin^2 - tanx

21. Sin^2x - 6sinx + 9/sin^2x - 9 = sinx-3/sinx+3

Especially the last three!

Answer 1

19). 4sin^2x/cos^2x - cos^2x/cos^2x

4(1-cos^2x) - cos^2x. All over cos^2x
4 - 4cos^2x - cos^2x. All over cos^2x
4 - 5cos^2x. All over cos^2x
4/cos^2x - 5

Answer 2

20). Sin^2x - sin x / cos x

(1-cos^2x)cos x - sin x. All over cos x
Cos x - cos^3x - sin x. All over cos x

Answer 3

21). Factor the numerator and the denominator

(Sin x - 3)(sin x - 3) / (sin x - 3)(sin x + 3)

Answer 4

17). Multiply numerator and denominator by
Sin x + 1

The numerator ( sin x + 1)(sin x -1) = sin ^2x -1
= -1(1 - sin^2x) = -cos^2x

Answer 5

18). Factor perfect square ( sin ^2x + cos^2x)^2
= 1^2=1