Secant is the inverse of cosine by definition, so secθ=1/cosθ, and (a) cosθsecθ=1 by cross-multiplication.
Cotangent is similarly the inverse of tangent (b).
Cosecant is similarly the inverse of sine (c).
Any trig function multiplied by its inverse is equal to 1.
In the case of tangent, cotθ=tan(90°-θ) also. (cot=adjacent/opposite=inverse of opposite/adjacent, that is, inverse of tan)