SOLUTION: Write each expression in terms of sines and/or cosines and then simplify. 1/sin^2(x)−1/tan^2(x) = cos(x)/sec(x)+cos^2(x) = sin(x)/csc(x)+cos^2(x) =

Algebra ->  Trigonometry-basics -> SOLUTION: Write each expression in terms of sines and/or cosines and then simplify. 1/sin^2(x)−1/tan^2(x) = cos(x)/sec(x)+cos^2(x) = sin(x)/csc(x)+cos^2(x) =       Log On


   

Question 1206826: Write each expression in terms of sines and/or cosines and then simplify.
1/sin^2(x)−1/tan^2(x)
=
cos(x)/sec(x)+cos^2(x) =
sin(x)/csc(x)+cos^2(x) =
Found 3 solutions by MathLover1, mananth, Edwin McCravy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

1%2Fsin%5E2%28x%29-1%2Ftan%5E2%28x%29
=1%2Fsin%5E2%28x%29-1%2F%28sin%5E2%28x%29%2Fcos%5E2%28x%29%29
=1%2Fsin%5E2%28x%29-cos%5E2%28x%29%2Fsin%5E2%28x%29
=%281-cos%5E2%28x%29%29%2Fsin%5E2%28x%29.....1-cos%5E2%28x%29=sin%5E2%28x%29
=sin%5E2%28x%29%2Fsin%5E2%28x%29
=1


cos%28x%29%2Fsec%28x%29%2Bcos%5E2%28x%29 ....use identity sec%28x%29=1%2Fcos%28x%29
=cos%28x%29%2F%281%2Fcos%28x%29%29%2Bcos%5E2%28x%29
=cos%28x%29%2Acos%28x%29%2Bcos%5E2%28x%29
=cos%5E2%28x%29%2Bcos%5E2%28x%29
=2cos%5E2%28x%29


sin%28x%29%2Fcsc%28x%29%2Bcos%5E2%28x%29 ....use identity csc%28x%29=1%2Fsin%28x%29
=sin%28x%29%2F%281%2Fsin%28x%29%29%2Bcos%5E2%28x%29
=sin%28x%29%2Asin%28x%29%2Bcos%5E2%28x%29
=sin%5E2%28x%29%2Bcos%5E2%28x%29
=1



Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
1/sin^2(x)−1/tan^2(x)
1%2Fsin%5E2%28x%29++-+cos%5E2%28x%29%2Fsin%5E2%28x%29
%281-cos%5E2%28x%29+%29%2Fsin%5E2%28x%29
sin%5E2%28x%29%2Fsin%5E2%28x+%29+
=1
cos(x)/sec(x)+cos^2(x) =
cos%28x%29%2F%28%281%2Fcosx%29%29+%2Bcos%5E2%28x%29
cos%5E2%28x+%29%2Bcos%5E2%28x%29
=2cos%5E2%28x%29


sin(x)/csc(x)+cos^2(x) =
sinx%2F%28%281%2Fsinx%29%29+%2Bcos%5E2%28x%29
sin%5E2%28x%29%2Bcos%5E2%28+x%29
=1

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fsin%5E2%28x%29-1%2Ftan%5E2%28x%29

csc%5E2%28x%29-cot%5E2%28x%29

Since 1%2Bcot%5E2%28theta%29=csc%5E2%28theta%29 is one of the standard identities:

1%2Bcot%5E2%28x%29-cot%5E2%28x%29

1

Edwin