SOLUTION: true or false. 1) sin θ = 1/cscθ, where sin θ ≠ 0. i thought it was true. 2) cos θ = 1/secθ, where cos θ ≠ 0. i thought it was true.

Algebra ->  Trigonometry-basics -> SOLUTION: true or false. 1) sin θ = 1/cscθ, where sin θ ≠ 0. i thought it was true. 2) cos θ = 1/secθ, where cos θ ≠ 0. i thought it was true.       Log On


   

Question 207158: true or false.
1) sin θ = 1/cscθ, where sin θ ≠ 0. i thought it was true.
2) cos θ = 1/secθ, where cos θ ≠ 0. i thought it was true.
thanks :]
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
They are both true. By definition, csc%28x%29=1%2Fsin%28x%29. If you solve for sin%28x%29, you get sin%28x%29=1%2Fcsc%28x%29


Similarly, sec%28x%29=1%2Fcos%28x%29. Isolating cos%28x%29 gets you cos%28x%29=1%2Fsec%28x%29


These identities are one of many which can be found here.