Multiply and simplify

Question

(cot x+1)^2 = simplify the answer

Answer 1

(cotx+1)² = (cotx+a)(cotx+1) = cot²x + 2cotx + 1 = csc²x + 2cotx

That might be the most simple form, with least terms

cot²x+1 = csc²x is an identity explaining the last step above

or sometimes a technique is to change everything into sines and cosines, which are in some respects are "simpler"

csc²x + 2cotx = 1/(sin²x) + 2cosx/sinx = (2cosxsinx+1)/sin²x

cscx = the inverse of sinx = 1/sinx and cotx = cosx/sinx

Answer 2

Hello Ayreeyon!

note that:

cotx = cosx/senx

(cotx +1)² = cot²x + 2cotx +1 = 1 + cot²x + 2cotx

1 + cot²x = 1 + (cosx/senx)² = (sen²x + cos²x)/sen²x = 1/sen²x = cosec²x

Then:

(cotx +1)² = cosec²x + 2cotx