find the exact value of the expression by using appropriate identities. do not use a calculator.\n\\frac{\\ta…

find the exact value of the expression by using appropriate identities. do not use a calculator.\n\\frac{\\tan 87^{\\circ}+\\tan 93^{\\circ}}{1 - \\tan 87^{\\circ}\\tan 93^{\\circ}}\n\\frac{\\tan 87^{\\circ}+\\tan 93^{\\circ}}{1 - \\tan 87^{\\circ}\\tan 93^{\\circ}}=\\square

find the exact value of the expression by using appropriate identities. do not use a calculator.\n\\frac{\\tan 87^{\\circ}+\\tan 93^{\\circ}}{1 - \\tan 87^{\\circ}\\tan 93^{\\circ}}\n\\frac{\\tan 87^{\\circ}+\\tan 93^{\\circ}}{1 - \\tan 87^{\\circ}\\tan 93^{\\circ}}=\\square

Answer

Explanation:

Step1: Recall the tangent addition formula

The formula for (\tan(A + B)=\frac{\tan A+\tan B}{1-\tan A\tan B}). In the given expression (\frac{\tan87^{\circ}+\tan93^{\circ}}{1 - \tan87^{\circ}\tan93^{\circ}}), we have (A = 87^{\circ}) and (B=93^{\circ}).

Step2: Calculate (A + B)

(A + B=87^{\circ}+93^{\circ}=180^{\circ}). So, (\frac{\tan87^{\circ}+\tan93^{\circ}}{1-\tan87^{\circ}\tan93^{\circ}}=\tan(87^{\circ}+93^{\circ})).

Step3: Evaluate (\tan(180^{\circ}))

We know that (\tan\theta=\frac{\sin\theta}{\cos\theta}), and (\sin(180^{\circ}) = 0), (\cos(180^{\circ})=- 1). So, (\tan(180^{\circ})=\frac{\sin(180^{\circ})}{\cos(180^{\circ})}=\frac{0}{-1}=0).

Answer:

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