Question

tan(A-B)=1/√3 and tan(A+B)=√3, Find A and B

Answer 1

Step-by-step explanation:

here A=45 and B=15 I hope it will help u

Answer 2

$\underline{ \huge\bf\red{QuestiØn} :}$

Given :-

• $\tan(A - B) = \dfrac{1}{ \sqrt{3} }$

• $\tan(A + B) = \sqrt{3}$

Find :-

• $\bf A \: \mathcal{and} \: B$

$\underline{ \: \huge\bf\green{SolutiØn} \: :}$

We have,

$\begin{aligned} \\& \quad \qquad \tan(A - B) = \frac{1}{ \sqrt{3} } \\ \\ & \implies \tan(A - B) = \tan(30 \degree) \\ \\ & \implies A - B = 30 \degree \ \ - - - - (i)\\ & \qquad \qquad \sf [comparing \: both \: the \: sides] \end{aligned}$

And,

$\begin{aligned} \\ & \quad \qquad \tan(A + B) = \sqrt{3} \\ \\ & \implies \tan(A + B) = \tan(60 \degree) \\ \\ & \implies A + B = 60 \degree \ \ - - - - (ii)\\ & \qquad \qquad\sf [comparing \: both \: the \: sides] \end{aligned}$

On solving equations ( i ) and ( ii ) , we get :—

• A = 45°

• B = 15°

$\red{\rule{5.8cm}{0.02cm}}$

$\mid \underline{\underline{\LARGE\bf\green{Brainliest \: Answer}}}\mid$