Question

If tan A = 1/2 and cot B = 3 then tan (A + B) =?​

Answer 1

$\huge\bigstar{\mathfrak{\underline{\green{Answer:-}}}}$

$\bigstar{\underline{\textbf{Given:-}}}$

tanA = 1/2

cotB = 3

$\bigstar$ According to trigonometry rule:-

tanB= 1/cotB

than,

$\large{\boxed{\tt{tan B= 1/3}}}$

$\huge\bigstar{\mathfrak{\underline{\green{Explanation:-}}}}$

$\bigstar$ Apply the trigonometry formula of tan(A+B)

tan(A+B)= tanA+tanB/1- tana × tanB

tan(A+B)=(1/2+1/3)/(1–1/3 × 1/2) ——> eq1

$\bigstar$ After solving the eq1 we get

tan(A+B)=(5/6) / (5/6)

both are cancel out then,

tan(A+B)=1 ———> eq2

$\bigstar{\underline{\textbf{Remember:-}}}$

After solution move the tan in right hand side then tan is change to arctan(1/tan)

A+B= arctan 1

arctan 1= π/4 or 45 degree

$\large{\boxed{\tt{Value \;of \;A+B= π /4 \;or \;45\; degree}}}$