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 $0$ .

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 $0$ .