SOLUTION: Can you prove each identity? And can you show me the solution so that I can do it next time? 1. (1+cos⁡θ)/cos⁡θ = sec θ + 1 2. cos⁡&#952

Algebra ->  Trigonometry-basics -> SOLUTION: Can you prove each identity? And can you show me the solution so that I can do it next time? 1. (1+cos⁡θ)/cos⁡θ = sec θ + 1 2. cos⁡&#952      Log On


   

Question 821467: Can you prove each identity? And can you show me the solution so that I can do it next time?
1. (1+cos⁡θ)/cos⁡θ = sec θ + 1
2. cos⁡θ/(1-sin⁡〖² θ〗 ) = sec θ
3. sec⁡〖θ-tan⁡θ 〗/sec⁡〖θ 〖+ tan〗⁡θ 〗 = (1-sin⁡θ)/(1+sin⁡θ )
4. 1/sec⁡〖θ-tan⁡θ 〗 + 1/sec⁡〖θ+tan⁡θ 〗 = 2sec θ
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
Prove each identity
1. (1+cos⁡θ)/cos⁡θ = sec θ + 1
2. cos⁡θ/(1-sin⁡〖² θ〗 ) = sec θ
3. sec⁡〖θ-tan⁡θ 〗/sec⁡〖θ 〖+ tan〗⁡θ 〗 = (1-sin⁡θ)/(1+sin⁡θ )
4. 1/sec⁡〖θ-tan⁡θ 〗 + 1/sec⁡〖θ+tan⁡θ 〗 = 2sec θ
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Rewrite Identities
use x in place of theta:
..
1.%281%2Bcos%28x%29%29%2Fcos%28x%29=sec%28x%29-1
start with left side:

verified: left side=right side
..
2.cos%28x%29%2F%281-sin%5E2%28x%29%29=sec%28x%29
start with left side:

..
3.
start with left side:
%28sec%28x%29-tan%28x%29%29%2F%28sec%28x%29%2Btan%28x%29%29
..

..

verified: left side=right side
..
4.%281%2F%28sec%28x%29-tan%28x%29%29%29%2B%281%2F%28sec%28x%29%2Btan%28x%29%29%29=2sec%28x%29
start with left side:
%281%2F%28sec%28x%29-tan%28x%29%29%29%2B%281%2F%28sec%28x%29%2Btan%28x%29%29%29
..

..
%28cos%28x%29%2F%281-sin%28x%29%29%29%2B%28cos%28x%29%2F%281%2Bsin%28x%29%29%29
..
%28cos%28x%29%281%2Bsin%28x%29%29%2Bcos%28x%29%281-sin%28x%29%29%29%2F%281-sin%5E2%28x%29%29
..

verified: left side=right side