The work for yesterday for question 7 tan(a-b) not tan(a+b)

Question

ScanSolve AI Tutor · Accepted Answer

Right fortune, let's correct that for you.

You are right, the previous solution calculated $\tan(A+B)$ . Let's calculate $\tan(A-B)$ for Question 7.

From the previous calculations:
$\tan A = \frac{5}{12}$
$\tan B = \frac{20}{21}$

Use the compound angle formula for $\tan(A-B)$ .
$\tan(A-B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$
Substitute the values of $\tan A$ and $\tan B$ .
$\tan(A-B) = \frac{\frac{5}{12} - \frac{20}{21}}{1 + \left(\frac{5}{12}\right)\left(\frac{20}{21}\right)}$
Calculate the numerator.
$\frac{5}{12} - \frac{20}{21} = \frac{5 \cdot 7}{12 \cdot 7} - \frac{20 \cdot 4}{21 \cdot 4} = \frac{35}{84} - \frac{80}{84} = \frac{35 - 80}{84} = \frac{-45}{84}$
Simplify the numerator by dividing by 3: $\frac{-15}{28}$ .
Calculate the denominator.
$1 + \left(\frac{5}{12}\right)\left(\frac{20}{21}\right) = 1 + \frac{100}{252}$
Simplify $\frac{100}{252}$ by dividing by 4: $\frac{25}{63}$ .
$1 + \frac{25}{63} = \frac{63}{63} + \frac{25}{63} = \frac{63 + 25}{63} = \frac{88}{63}$
Divide the numerator by the denominator.
$\tan(A-B) = \frac{\frac{-15}{28}}{\frac{88}{63}} = \frac{-15}{28} \times \frac{63}{88}$
Simplify by dividing 28 and 63 by their common factor 7:
$28 \div 7 = 4$ $63 \div 7 = 9$ $\tan(A-B) = \frac{-15}{4} \times \frac{9}{88} = \frac{-135}{352}$
The value of $\tan(A-B)$ is $\boxed{\frac{-135}{352}}$ .

Answer