Mathematics

Problem

Answer the following questions related to the fundamental trigonometric identities. a. (i) Starting with the identity

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

, derive the identity

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

step by step. b. (ii) Give a brief explanation, in words, of why the identity you have derived in part (i) holds true for every acute angle

\theta

for which

\tan\theta

and

\sec\theta

are defined.