Mathematics

Problem

For an angle

\theta

in the second quadrant it is given that

\sec\theta + \tan\theta = -2

. Answer the following: a. (i) Prove that

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

. b. (ii) Hence find the exact values of

\sec\theta

and

\tan\theta

. c. (iii) Using the results of part (ii), determine

\sin\theta,\;\cos\theta,\;\csc\theta

and

\cot\theta

. d. (iv) Confirm that

\sin^{2}\theta + \cos^{2}\theta = 1

for the obtained values.