Step 1 :1.1 \(\sin\theta = \frac{4}{5}, \csc\theta = \frac{5}{4}, \sin\theta\cdot\csc\theta = \frac{4}{5} \cdot \frac{5}{4} = 1\)
Step 2 :1.2 \(\tan\theta = -\frac{4}{3}, \cot\theta = -\frac{3}{4}, \tan\theta\cdot\cot\theta = -\frac{4}{3} \cdot -\frac{3}{4} = 1\)
Step 3 :1.3 \(\cos\theta = \frac{1}{\sqrt{2}}, \sec\theta = \sqrt{2}, \cos\theta\cdot\sec\theta = \frac{1}{\sqrt{2}} \cdot \sqrt{2} = 1\)
Step 4 :1.4 \(\sin\theta = \frac{\sqrt{3}}{2}, \csc\theta = \frac{2}{\sqrt{3}}, \sin\theta\cdot\csc\theta = \frac{\sqrt{3}}{2} \cdot \frac{2}{\sqrt{3}} = 1\)
Step 5 :1.5 \(\tan\theta\sin\theta\cot\theta = \tan\theta\cdot (1)(\cot\theta) = \tan\theta\cdot\cot\theta = 1\)
Step 6 :1.6 \(\frac{1}{\cos\theta\sec\theta} \cdot \cot\theta = \frac{\cot\theta}{\cos\theta\sec\theta} = \cot\theta \div 1 = \cot\theta\)
Step 7 :1.7 \(1+\tan\theta\cot\theta-\frac{\sin\theta\csc\theta}{2} = 1 + 1 - \frac{1}{2} = \frac{3}{2}\)
Step 8 :1.8 \(\frac{\sin\theta}{\csc\theta} = \frac{\sin\theta}{\frac{1}{\sin\theta}} = \frac{\sin\theta}{1}(\sin\theta) = \sin^2\theta\)
Step 9 :1.9 \(\frac{\tan\theta}{\cot\theta} = \frac{\tan\theta}{\frac{1}{\tan\theta}} = \tan^2\theta\)
Step 10 :1.10 \(\frac{\sec\theta}{\cos\theta} = \frac{\sec\theta}{\frac{1}{\sec\theta}} = \sec^2\theta\)