Mathematics

Problem

For an acute angle

\theta

it is given that

\tan\theta + \sec\theta = \sqrt{3}

. Work through the steps below. a. (i) Rewrite the given relation so that it involves

\tan\theta

only. b. (ii) Solve the resulting quadratic equation to obtain all possible value(s) of

\tan\theta

. c. (iii) Using the value of

\tan\theta

, determine the corresponding values of

\sin\theta

and

\cos\theta

. d. (iv) Show that the values found satisfy

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