SOLUTION: Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression cot^2x(1+tan^2x)?

Algebra ->  Trigonometry-basics -> SOLUTION: Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression cot^2x(1+tan^2x)?      Log On


   

Question 953101: Write the expression in terms of sine and cosine, and simplify so that no quotients appear in the final expression cot^2x(1+tan^2x)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
cot%5E2%28x%29%281%2Btan%5E2%28x%29%29 ............since cot%5E2%28x%29=cos%5E2%28x%29%2Fsin%5E2%28x%29 and tan%5E2%28x%29=sin%5E2%28x%29%2Fcos%5E2%28x%29, we have

=%28cos%5E2%28x%29%2Fsin%5E2%28x%29%29%281%2Bsin%5E2%28x%29%2Fcos%5E2%28x%29%29

=

=

=cos%5E2%28x%29%2Fsin%5E2%28x%29%2B1

=cos%5E2%28x%29%2Fsin%5E2%28x%29%2B1%2Asin%5E2%28x%29%2Fsin%5E2%28x%29

=%28cos%5E2%28x%29%2Bsin%5E2%28x%29%29%2Fsin%5E2%28x%29

=1%2Fsin%5E2%28x%29
=sin%5E-2%28x%29 -> in terms of sine
or, we can use identity 1%2Fsin%5E2%28x%29=csc%5E2%28x%29

=csc%5E2%28x%29