Question

TRIG PROBLEM! i give medals.
prove the identity is true:

Answer 1

\[\sin ^{2}x (\cot ^{2}x+1) = 1\]

Answer 2

Since cot(x) = 1/tan(x) and tan(x) = sin(x)/cos(x) then

sin^2(x)*(1 + cot^2(x)) = sin^2(x)*(1 + cos^2(x)/sin^2(x)) = sin^2(x) + cos^2(x) = 1
since sin^2(x) + cos^2(x) =1

Answer 3

ok one sec

Answer 4

okay @sophiaedge , that makes sense, what next?

Answer 5

Mmmm I don't know I emailed that to my friend and that's all he sent back sorry!

Answer 6

aw okay thanks

Answer 7

can anyone explain this to me? :(

Answer 8

\[\sin ^{2}x (\cot ^{2}x+1) = 1\]\[\sin^2(x)\left(\frac{\cos^2(x)}{\sin^2(x)} +1\right) = 1\]\[\sin^2\cdot \frac{\cos^2(x)}{\sin^2(x)} + \sin^2(x) = 1\]\[\cancel{\sin^2(x)}\cdot \frac{\cos^2(x)}{\cancel{\sin^2(x)}} + \sin^2(x) = 1\]\[\cos^2(x) + \sin^2(x)=1\]\[\boxed{1 = 1}~~\checkmark\]

Answer 9

oh my god. i love you.

Answer 10

i have one more, i will post in a different question, is that okay?

Answer 11

that way i can give you a medal.. id give you a trophy if i could, but i can only do medals

Answer 12

Haha, sure. although @sophiaedge is the one who originally solved it :P