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Magazine Problem 1
In Exercises 1-20, simplify each of the following trigonometric expressions. $$ \sin x \csc x $$
Problem 2
In Exercises 1-16, use the half-angle identities to find the exact values of the trigonometric expressions. $$ \cos \left(22.5^{\circ}\right) $$
Problem 4
Simplify each of the following trigonometric expressions. $$ \tan (-x) \cos (-x) $$
Problem 5
Use the half-angle identities to find the exact values of the trigonometric expressions. $$ \cos 75^{\circ} $$
Problem 7
Simplify each of the following trigonometric expressions. $$ (\sin x-\cos x)(\sin x+\cos x) $$
Problem 10
Find exact values for each trigonometric expression. $$ \cos 195^{\circ} $$
Problem 12
Use the half-angle identities to find the exact values of the trigonometric expressions. $$ \tan \left(202.5^{\circ}\right) $$
Problem 17
Simplify each of the following trigonometric expressions. $$ \frac{\cot ^{2} x+1}{\csc x}-\csc x $$
Problem 20
Simplify each of the following trigonometric expressions. $$ \frac{\cot ^{2} x}{\csc x}-\csc x $$
Problem 22
In Exercises 21-46, verify each of the trigonometric identities. $$ (1-\sin x)(1+\sin x)=\cos ^{2} x $$
