Question

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

Answer 1

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. 

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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