Find the exact value of the expression. Do not use a calculator.
\[
\tan 69^{\circ}-\frac{\cos 21^{\circ}}{\cos 69^{\circ}}
\]

Answer

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Answer

So, the exact value of the expression is \(\boxed{0}\).

Steps

Step 1 ：We have that

Step 2 ：\[\tan 69^\circ - \frac{\cos 21^\circ}{\cos 69^\circ} = \tan 69^\circ - \frac{\sin 69^\circ}{\cos 69^\circ}\]

Step 3 ：Since \(\tan x = \frac{\sin x}{\cos x}\), we can rewrite the expression as

Step 4 ：\[\tan 69^\circ - \tan 69^\circ = 0\]

Step 5 ：So, the exact value of the expression is \(\boxed{0}\).