Mathematics

Problem

Answer the questions below about fundamental trigonometric identities. a. (i) Starting with

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

, derive the identity

1 + \cot^{2}\theta = \csc^{2}\theta

. b. (ii) For an acute angle

\theta

where

\cot\theta = \dfrac{7}{24}

, compute

\csc\theta

. c. (iii) Verify numerically that the values in part (ii) satisfy the identity obtained in part (i). d. (iv) Using the same angle, determine

\sin\theta

and

\cos\theta