Welcome to Westonci.ca, the place where your questions find answers from a community of knowledgeable experts. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

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

Sagot :

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 


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 


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 
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. We appreciate your visit. Our platform is always here to offer accurate and reliable answers. Return anytime. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.