MHT CET · Maths · Trigonometric Equations
If \(\tan A=\frac{1}{2}, \tan B=\frac{1}{3}\) then \(\tan (A+2 B)\) has the value
- A 2
- B 3
- C 4
- D 1
Answer & Solution
Correct Answer
(A) 2
Step-by-step Solution
Detailed explanation
\(\tan A=\frac{1}{2}, \tan B=\frac{1}{3}\)
[given] we have \(\tan 2 B=\frac{2 \tan B}{1-\tan ^2 B}=\frac{3}{4}\)
\(\because \tan (A+2 B)=\frac{\tan A+\tan 2 B}{1-\tan A \cdot \tan 2 B}=\frac{\frac{1}{2}+\frac{3}{4}}{1-\frac{1}{2} \times \frac{3}{4}}=\frac{\frac{5}{4}}{\frac{5}{8}}=2\)
[given] we have \(\tan 2 B=\frac{2 \tan B}{1-\tan ^2 B}=\frac{3}{4}\)
\(\because \tan (A+2 B)=\frac{\tan A+\tan 2 B}{1-\tan A \cdot \tan 2 B}=\frac{\frac{1}{2}+\frac{3}{4}}{1-\frac{1}{2} \times \frac{3}{4}}=\frac{\frac{5}{4}}{\frac{5}{8}}=2\)
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