Question

differentiate and simplify
csc^2 theta
+ cot^2 theta

Answer 1

Remember that \[\csc ^{2}\] is just =\[-\cot ^{2}(\theta)\csc ^{2}(\theta)\]

Answer 2

got that part. then what?

Answer 3

Let's say that theta = x, also note that 1+cot^2x=csc^2x

d/dx[csc^2x-cot^2x] =
= -cot^xcsc^2x-csc^2x =
= -csc^2x(cot^2x+1) =
= csc^x(csc^2x) =
= -csc^4x

the answer is -csc^4(theta)

Answer 4

thanks!