this has to do with proving identities in trigonometric functions. Please answer all of the questions and please show all of your work so it is easier to understand. (Also in some questions "/" means it is a fraction)

1) Simplify the rational trigonometric function without substitution, just factor. If the denominator is eliminated place a 1 in its answer box.

sinxcosx-sinx/cos²x-1

numerator=

denominator=

2)Simplify the rational trigonometric function without substitution, just factor. If the denominator is eliminated place a 1 in its answer box.

cos²x-cosx-2/6cosx-12

numerator=

denominator=

3)Simplify the rational trigonometric function without substitution, just factor. If the denominator is eliminated place a 1 in its answer box.

sinx-sinxcosx²x/sin²x

numerator=

denominator=

4)Simplify the rational trigonometric function without substitution, just factor. If the denominator is eliminated place a 1 in its answer box.

tan²x-3tanx-4/sinxtanx+sinx

numerator=

denominator=

5)Prove the identity.

cosx+cosxtan² x=secx

1=

2=

6)Prove the identity.

sinx²-cos²x/sinx+cosx= sinx-cosx

1=

2=

7)Prove the identity.

1-cos² x=tanxcosx/cscx

1=

2=

3=

4=

8)Prove the identity.

cosx(secx-cosx)=sin²x

1=

2=

3=

4=

9)Prove the identity.

sin²x=(1-cosx)(1+cosx)

1=

2=

3=

4=

10)Prove the identity.

1/1+sinx=secx-sinxsecx/cosx

1=

2=

3=

4=

11)Prove the identity.

sec²xtan²x-tan² x=tan⁴x

1=

2=

3=

4=

12)Prove the identity.

sinx+cosxcotx=cscx

1=

2=

3=

4=

5=

13)Prove the identity.

(cscx-1)(cscx+1)=cot²x

1=

2=

3=

4=

5=

14)Prove the identity.

tan x= sin2x/cos2x+1

1=

2=

3=

4=

5=