Mathematics

Problem

Let

\alpha

be an obtuse angle such that

\sin \alpha = \dfrac{7}{25}

. a. (i) Calculate

\cos \alpha

and

\tan \alpha

. b. (ii) Determine

\sec \alpha

and

\cot \alpha

. c. (iii) Show by direct substitution that

1 + \tan ^2\!\alpha = \sec ^2\!\alpha