Question

if tan (A+B) =1 and tan (A-B) = 1/ root3 find A and B​

Answer 1

Answer:

tan(A+B) = 1

tan 45 = 1

A+B = 45

tan(A-B) = 1/√3

tan 30 = 1/√3

A-B = 30

By elimination

2A = 75°

A = 75/2 = 37.5°

37.5+B = 45°

B = 7.5°

Answer 2

•Given→

$\tan(a + b) = 1$

$\tan(a - b) = \frac{1}{ \sqrt{3} }$

• To find→

$value \: of \: a \: and \: b$

•Solution→

•

$\tan(a + b) = 1\\ = > \tan(a + b) = \tan(45) \\ = > a + b = 45..........(i)$

•

$\tan(a - b) = \frac{1}{ \sqrt{3} } \\ = > \tan(a - b) = \tan(30) \\ = > a - b = 30..........(ii)$

★ By elimination→

$a + b = 45.........(i) \\ a - b = 30 .........(ii)$

_________________

$= > 2a = 75 \\ = > a = \frac{75}{2 } \\ = > a = 37.5$

★Put the value of “a” in the (i) equation.

$a + b = 45 \\ = > 37.5 + b = 45 \\ = > b = 45 - 37.5 \\ = > b = 7.5$

★ Value of “A” = 37.5

★ Value of “B” = 7.5

• Answer→

Value of“A” = 37.5

Value of“B” = 7.5