Question

given that tanA=1/2,cotB=3 then the value of A+B is ... ?​

Answer 1

Find the value of A+B:

Step-by-step explanation:

$\ Given \ value:\\\\\tan A = \frac{1}{2}\\\\\cot B= 3\\\\\ find: \\\\A+B= ?\\\\\ Solution:\\\\\tan A = \frac{1}{2}\\\\\cot B= 3\\\\\ change \cot B \ to \tan B\\\\\cot B= \frac{1}{\tan B}\\\\ \tan B= \frac{1}{\cot B}\\\\\tan B= \frac{1}{3}\\\\\tan A=\frac{1}{2}\\\\\ formula:\\\\\tan (A+B) = \frac{\tan A \ + \tan B}{1- \tan A\tan B}\\\\\rightarrow \tan (A+B) = \frac{\frac{1}{2} \ +\frac{1}{3}}{1- \frac{1}{2}\frac{1}{3}}$

$\rightarrow \tan (A+B) = \frac{\frac{3+2}{6}}{1- \frac{1}{6}}}\\\\\rightarrow \tan (A+B) = \frac{\frac{5}{6}}{\frac{6-1}{6}}}\\\\\rightarrow \tan (A+B) = \frac{\frac{5}{6}}{\frac{5}{6}}}\\\\\rightarrow \tan (A+B) = \frac{5}{6} \times \frac{6}{5}\\\\\rightarrow \tan (A+B) = 1\\\\\rightarrow \tan (A+B) = \tan 45^{\circ}\\\\\rightarrow (A+B) = 45^{\circ}$

Learn more:

• Prove: https://brainly.in/question/14282720