Mathematics

Problem

Suppose

\tan\theta = \dfrac{7}{24}

and

\theta

is an angle in the third quadrant. Complete the tasks below: a. (i) Determine

\sin\theta,\;\cos\theta

and

\sec\theta

. b. (ii) Evaluate the numerical value of the expression

E = \sec\theta - \csc\theta

. c. (iii) Show that

\sec^{2}\theta - \tan^{2}\theta = 1

for this angle.