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.

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

cos2x1sinxcosxsinx

numerator=

denominator=

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

6cosx12cos2xcosx2

numerator=

denominator=

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

sin2xsinxsinxcos2x

numerator=

denominator=

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

sinxtanx+sinxtan2x3tanx4

numerator=

denominator=

5)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

cosx+cosxtan² x=secx

Left side

=1(1+tan2X)

=cosx2

=cosx(31)

=cosx1

=secx

1=

2=

3=

6)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

sinx+cosxsinx2cosx2=sinxcosx

left side

=sinx+cosx(1)(2)

=2

1=

2=

7)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

1cos2x=cscxtanxcosx

right side

(2)(1)cos2

=23

=3x3

=4

=1-cos²x

1=

2=

3=

4=

8)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

cosx(secx-cosx)=sin²x

left side

=cosx(1cosx1)

=23

=4

1=

2=

3=

4=

9)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

sin²x=(1-cosx)(1+cosx)

Right side

=1+234

=14

=5

=left side

1=

2=

3=

4=

5=

10)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

1/1+sinx=secx-sinxsecx/cosx

Right side

=cosxsecx(1)

=cosx(2)(1)

=3cosx(1)

=cos2x(1)

=(1)(4)(1)

=1+sinx1

1=

2=

3=

4=

11)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

sec²xtan²x-tan² x=tan⁴x

Left side

=1(23)

=1(4)

=tan⁴x

=right side

1=

2=

3=

4=

12)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

sinx+cosxcotx=cscx

left side

=sinx+cosx(1)

=sinx+sinx2

=(3)sinx+sinx2

=sinx4+2

=sinx5

=cscx

1=

2=

3=

4=

5=

13)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

(cscx-1)(cscx+1)=cot²x

left side

=1+234

=14

=5

=left side

1=

2=

3=

4=

5=

14)Prove the identity.The numbers that are in blue below correspond to the answer box. the 1 in blue is to go in answer 1 and so on. If the brackets are in parentheses, it is a hint to you that the expression that belongs in it is either more than one term or a fraction. Use ^ to denote exponents, that is sin^2x represents sin²x.

tanx=cos2x+1sin2x

right side

(2)+11

=31

=54

=tanx

1=

2=

3=

4=

5=