Mathematics

Problem

\triangle XYZ

, right-angled at

Y

, the length of

XY

3k

units and the length of

YZ

4k

units, where

k

is a positive real number. a. (i) Express the length of the hypotenuse

XZ

in terms of

k

. b. (ii) For

\angle XZY = \gamma

, obtain simplified algebraic expressions for

\sin \gamma

\cos \gamma

and

\tan \gamma

. c. (iii) Show that

\sec \gamma - \cos \gamma = \dfrac{9}{20}

, independent of the value of

k