Simplify each expression to be an integer or single trig function by using trig identities and Pythagorean identities.
1) \(\large{\frac{1}{\cos^2\theta}}-\normalsize\cos^2\theta\sec^2\theta\)
2) \(1+\large{\frac{\cos^2\theta}{\cot^2\theta}}-\normalsize\sin^2\theta\)
3) \(\left(1-\cos\theta\right)\left(1+\cot^2\theta\right)\left(1+\cos\theta\right)\)
4) \(\csc^2\theta\cos^2\theta-\large\frac{\cot\theta}{\sin\theta\cos\theta}\)
5) \(\cos^2\theta+\sec^2\theta+\sin^2\theta-\tan^2\theta\)
6) \(\left(\sin\left(-\theta\right)\right)\cot\theta\)
7) \(\left(\left(\cos^2\theta-1\right)\cot^2\theta\right)\sec\theta\)
8) \(\Large\frac{1+\tan^2\theta}{\sec^2\theta}-\frac{1}{\sec^2\theta}\)
9) \(\Large\frac{\tan^{ }\theta}{\sec^2\theta}\cdot\frac{\cot\theta}{\sin^2\theta}\)
10) \(\cos^2\theta+\tan\theta\sin\theta\cos\theta\)
Solution Bank
1) \(\large{\frac{1}{\cos^2\theta}}-\normalsize\cos^2\theta\sec^2\theta\)
2) \(1+\large{\frac{\cos^2\theta}{\cot^2\theta}}-\normalsize\sin^2\theta\)
3) \(\left(1-\cos\theta\right)\left(1+\cot^2\theta\right)\left(1+\cos\theta\right)\)
4) \(\csc^2\theta\cos^2\theta-\large\frac{\cot\theta}{\sin\theta\cos\theta}\)
5) \(\cos^2\theta+\sec^2\theta+\sin^2\theta-\tan^2\theta\)
6) \(\left(\sin\left(-\theta\right)\right)\cot\theta\)
7) \(\left(\left(\cos^2\theta-1\right)\cot^2\theta\right)\sec\theta\)
8) \(\Large\frac{1+\tan^2\theta}{\sec^2\theta}-\frac{1}{\sec^2\theta}\)
9) \(\Large\frac{\tan^{ }\theta}{\sec^2\theta}\cdot\frac{\cot\theta}{\sin^2\theta}\)
10) \(\cos^2\theta+\tan\theta\sin\theta\cos\theta\)
Solution Bank