Question

If tan (A+B) = root 3 and (A - B) = 1/root 3; 0°<A+B <or equal to 90°; A>B , find A and B.

Answer:- A = 45° and B = 15°.

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Answer 1

$tan(a + b) = \sqrt{3} \\ \\ = > tan(a + b) = tan60 \: \: \: \: \: \: \: (tan60 = \sqrt{3} ) \\ \\ tan \: get \: cancelled \: on \: both \: sides \\ \\ = > (a + b) = 60 - - - (1) \\ \\ given \: tan(a - b) = \frac{1}{ \sqrt{3} } \\ \\ = > tan(a - b) = tan30 \: \: \: \: \: \: (tan30 = \frac{1}{ \sqrt{3} } ) \\ \\ tan \: gets \: cancelled \: on \: both \: sides \\ \\ = > (a - b) = 30 - - - (2) \\ \\ adding \: eq(1) \: and \: eq(2) \\ \\ = > a + b = 60 \\ \: \: \: \: \: \: \: \: \: a - b = 30 \\ - - - - - - - - - - - - \\ = > 2a = 90 \\ \\ = > a = 45 \\ \\ from \: eq(1) \\ \\ 45 + b = 60 \\ \\ = > b = 15$

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Answer 2

Answer:

tan (a+b)= √3

tan a+b= 60 tan=60 (tan60= tan get cancelled on both sides

a+b=60 _ _ _ (1)

given tan (a-b) = 1

√13

tan (a-b) =30 (tan30=

tan gets cancelled on both sides

(a-b)=30_ _ _ (2)

adding eq(1) and eq(2)

a+b=60

a-b=30

2a = 90

a=45

from eq(1)

45+b=60

b = 15 is the answer

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