Question

What is a simplified form of the expression cos^3(theta) + cos(theta)/csc^2(theta)

Answer 1

cos^3 T + cos T/csc^2 T
csc = 1/sin
so
cos^3 T + cos T sin^2 T
oh my look
cos T ( cos^2 T + sin^2 T) but we all know what cos^2+sin^2 is !

Answer 2

very confused lol

Answer 3

cos T ( ONE) = cos T
cos^2 angle + sin^2 angle = ONE

in right triangle
c^2 = a^2 + b^2
cos angle at A = b/c
sin angle at A = a/c
so cos^2 a = b^2/c^2
and sin^2 a = a^2/c^2
sum = a^2/c^2 + b^2/c^2 = (a^2+b^2)/c^2
but c^2 = a^2+b^2
SO
sum = (a^2+b^2) /(a^2+b^2) = ONE !!!!