These have to do with Trigonometric Identities and demonstrating an understanding of trigonometric identities including: reciprocal identities, quotient identities, Pythagorean identities, sum or difference identities, and double angle identities. please answer ALL of the questions and please show all of your work so it is easier to understand. (Also the "/" in some questions means it is a fraction)

1)Write each expression as a single trigonometric function.

1-2cos²(pi/12)

=

2)Write each expression as a single trigonometric function.

cos²(pi/4)-sin²(pi/4)

=

3)Write each expression as a single trigonometric function.

2cos²41degrees-1

=

4)Write each expression as a single trigonometric function.

cos²19degrees-sin²19degrees

=

5)Write each expression as a single trigonometric function.

2sin18degreescos18degrees

=

6)Write each expression as a single trigonometric function.

1-2sin²27degrees

=

7)Write each expression as a single trigonometric function.

1-2sin²(pi/2)

=

8)Simplify to a single trigonometric function then determine the exact value of it.

cos40degreescos20degrees-sin40degreessin20degrees

trig function=

exact value=

9)Simplify to a single trigonometric function then determine the exact value of it.

sin (pi/2)cos (pi/3) - cos (pi/2) sin (pi/3)

trig function=

exact value=

10)Simplify to a single trigonometric function then determine the exact value of it.

sin 20degrees cos 25degrees + cos 20 degrees sin 25 degrees

trig function=

exact value=

11)Simplify to a single trigonometric function then determine the exact value of it.

cos² (pi/6) - sin² (pi/6)

trig function=

exact value=

12)Simplify to a single trigonometric function then determine the exact value of it.

sin 80degrees cos 20degrees - cos 80degrees sin 20degrees

trig function=

exact value=

13) determine the exact value for each trigonometric expression

cos 195degrees

=

14)determine the exact value for each trigonometric expression

sin (7pi/12)

=

15)determine the exact value for each trigonometric expression

sin (-pi/12)

=

16)determine the exact value for each trigonometric expression

tan 105degrees

=

17)determine the exact value for each trigonometric expression

cos 75degrees

=

18) determine the exact value for each trigonometric expression

tan 165degrees

=

19)Simplify each expression to a single primary trigonometric function.

cos2x+1/2cosx

20)Simplify each expression to a single primary trigonometric function.

cos³x/cos2x+sin²x

=

21)Simplify each expression to a single primary trigonometric function.

sin2x/2cosx

22)Simplify each expression to a single primary trigonometric function.

cos2xcosx+sin²xsinx

=

23)If (sinx+cosx)²=k what is the value of sin2x in terms of k?

24) What value of k makes the following true?

sin5xcosx+cos5xsinx=2sin kx cos kx

=