Trigonometric Identities

See the steps toward proving a trigonometric identity:

(1 + tan(x))/(1 – tan(x)) = (cos(x) + sin(x))/(cos(x) – sin(x))

cot(t/2)^2 = (1 + cos(t)) / (1 – cos(t))

Mathematical Induction

Prove a sum identity by induction:

prove by induction sum of j from 1 to n = n(n+1)/2 for n>0

Prove divisibility by induction:

using induction, prove 9^n-1 is divisible by 4 assuming n>0

Prove an inequality by induction:

prove by induction (3n)! > 3^n (n!)^3 for n>0