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Simplify each expression to a single trig function or number cosx(secx-cosx)

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I did this test b4, yours is answer #number 12

Convert things to their basic forms.
Remember a few identities
sin^2 + cos^2 = 1 so
sin^2 = 1 - cos^2 and
cos^2 = 1 - sin^2

I'm going to skip typing the theta symbol, just to make things faster. Just assume it is there and fill it in as you work the problems.

Follow along to see how each problem was worked out. You'll catch on to the general technique.

======
1. sec θ sin θ
1/cos * sin = sin/cos = tan

2. cos θ tan θ
cos * sin/cos = sin

3. tan^2 θ- sec^2 θ
sin^2 / cos^2 - 1/cos^2
(sin^2 - 1)/cos^2
-(1-sin^2)/cos^2
-cos^2/cos^2
-1

4. 1- cos^2θ
sin^2

5. (1-cosθ)(1+cosθ)
Remember (a+b)(a--b) = a^2 - b^2
1-cos^2 = sin^2

6. (secx-1) (secx+1)
sec^2 -1
1/cos^2 - 1
1/cos^2 - cos^2/cos^2
(1-cos^2)/cos^2
sin^2/cos62
tan^2

7. (1/sin^2A)-(1/tan^2A)
1/sin^2 - 1/(sin^2/cos^2)
1/sin^2 - cos^2/sin^2
(1-cos^2)/sin^2
sin^2/sin^2
1

8. 1- (sin^2θ/tan^2θ)
1-sin^2/(sin^2/cos^2)
1 - sin^2*cos^2/sin^2
1-cos^2
sin^2


9. (1/cos^2θ)-(1/cot^2θ)
1/cos^2 - 1/(cos^2/sin^2)
1/cos^2 - sin^2/cos^2
(1-sin^2)/cos^2
cos^2/cos^2
1

10. cosθ (secθ-cosθ)
cos *(1/cos - cos)
1-cos^2
sin^2

11. cos^2A (sec^2A-1)
cos^2 * (1/cos^2 - 1)
1 - cos^2
sin^2


12. (1-cosx)(1+secx)(cosx)
(1-cos)(1+1/cos)cos
(1-cos)(cos + 1)
-(cos-1)(cos+1)
-(cos^2 - 1)
-(-sin^2)
sin^2

13. (sinxcosx)/(1-cos^2x)
sin*cos/sin^2
cos/sin
cot

14. (tan^2θ/secθ+1) +1
(sin^2/cos^2)/(1/cos) + 2
sin^2/cos + 2
sin*tan + 2
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