Two functions f and g are defined as follows: Determine, with reasons, whether fg and gf exist. If the composite function exists, give the rule, domain and range in exact form.

In triangle PQR, angle radians and angle . Given that is sufficiently small for and above to be ignored, show that

Express as partial fractions and hence obtain f(x) as a series in ascending powers of x as far as the term x³. State the range of values of x for which the expansion is valid. Find the coefficient of in the expansion, where n>1.