For an acute angle it is given that

MATHEMATICS · Multi-part · CBSE · Mathematics · Introduction to Trigonometry · Introduction to Trigonometry

Problem

For an acute angle

\theta

it is given that

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

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

\tan\theta

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

\tan\theta

. (iii) Using the value of

\tan\theta

, determine the corresponding values of

\sin\theta

and

\cos\theta

. (iv) Show that the values found satisfy

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