Mathematics

Problem

Let

\theta

be an angle satisfying

\sin\theta=\dfrac{3}{5}

and

\dfrac{\pi}{2}<\theta<\pi

. a. (i) Calculate

\cos\theta

and

\tan\theta

. Give exact values with correct signs. b. (ii) Compute

\sin\theta+\cos\theta

and

\sin\theta\,\tan\theta

. c. (iii) Verify that

(\sin\theta+\cos\theta)^2+(\sin\theta-\cos\theta)^2=2

for this value of

\theta

. Present each step clearly.