Math (trigonometric identities)
posted by Kim on .
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. Sinx1/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 = sinx3/sinx+3
Especially the last three!

19). 4sin^2x/cos^2x  cos^2x/cos^2x
4(1cos^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 
20). Sin^2x  sin x / cos x
(1cos^2x)cos x  sin x. All over cos x
Cos x  cos^3x  sin x. All over cos x 
21). Factor the numerator and the denominator
(Sin x  3)(sin x  3) / (sin x  3)(sin x + 3) 
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 
18). Factor perfect square ( sin ^2x + cos^2x)^2
= 1^2=1