SOLUTION: write the given expression in one term only. 1. cot^2 theta (csc theta) in terms of sin theta 2. 1-csc^2 theta / csc^2 in terms of cos theta

Algebra ->  Trigonometry-basics -> SOLUTION: write the given expression in one term only. 1. cot^2 theta (csc theta) in terms of sin theta 2. 1-csc^2 theta / csc^2 in terms of cos theta      Log On


   

Question 1011295: write the given expression in one term only.
1. cot^2 theta (csc theta) in terms of sin theta
2. 1-csc^2 theta / csc^2 in terms of cos theta
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
1. cot%5E2+%28theta+%29%28csc+theta%29 in terms of sin%28+theta+%29
since
cot%5E2+%28theta%29+=cos%5E2%28theta%29%2Fsin%5E2%28theta%29 and
csc+%28theta%29=1%2Fsin%28theta%29, we have



since cos%5E2%28theta%29=1-sin%5E2%28theta%29, we have







2.
if you have
%281-csc%5E2+%28theta+%29%29%2F+csc%5E2++%28theta+%29 , in terms of cos+%28theta+%29 will be:
since 1%2F+csc%5E2++%28theta+%29=sin%5E2%28theta%29, we will have


since csc%5E2+%28theta+%29=1%2Fsin%5E2%28theta%29, we will have





%281-csc%5E2+%28theta+%29%29%281%2F+csc%5E2++%28theta+%29%29+=sin%5E2%28theta%29-1

%281-csc%5E2+%28theta+%29%29%281%2F+csc%5E2++%28theta+%29%29+=-%281-sin%5E2%28theta%29%29

%281-csc%5E2+%28theta+%29%29%2F+csc%5E2++%28theta+%29+=-cos%5E2%28theta%29