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Magazine Problem 84
For the following exercises, find the exact value algebraically, and then confirm the answer with a calculator to the fourth decimal point. \(\sin \left(75^{\circ}\right)\)
Problem 85
For the following exercises, find the exact value algebraically, and then confirm the answer with a calculator to the fourth decimal point. \(\sin \left(195^{\circ}\right)\)
Problem 86
For the following exercises, find the exact value algebraically, and then confirm the answer with a calculator to the fourth decimal point. \(\cos \left(165^{\circ}\right)\)
Problem 87
For the following exercises, find the exact value algebraically, and then confirm the answer with a calculator to the fourth decimal point. \(\cos \left(345^{\circ}\right)\)
Problem 88
For the following exercises, find the exact value algebraically, and then confirm the answer with a calculator to the fourth decimal point. \(\tan \left(-15^{\circ}\right)\)
Problem 89
For the following exercises, prove the identities provided. $$ \tan \left(x+\frac{\pi}{4}\right)=\frac{\tan x+1}{1-\tan x} $$
Problem 90
For the following exercises, prove the identities provided. $$ \frac{\tan (a+b)}{\tan (a-b)}=\frac{\sin a \cos a+\sin b \cos b}{\sin a \cos a-\sin b \cos b} $$
Problem 91
For the following exercises, prove the identities provided. $$ \frac{\cos (a+b)}{\cos a \cos b}=1-\tan a \tan b $$
Problem 92
For the following exercises, prove the identities provided. $$ \cos (x+y) \cos (x-y)=\cos ^{2} x-\sin ^{2} y $$
Problem 95
For the following exercises, prove or disprove the statements. $$ \tan (u-v)=\frac{\tan u-\tan v}{1+\tan u \tan v} $$
