Question

if tan(a+b)=1 and tan (a-b)=1/squareroot 3 , then find value of a and b​

Answer 1

$\tan(a - b) = \tan(45 ) \\ \tan(a - b) = \tan(30) \\ a + b = 45 \\ a - b = 30 \\ 2a = 75 \\ a = 37.5 \\ b = 45 - 37. 5 \\ b = 7.5$

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Answer 2

Answer
tan (a+b)=tan45
a+b=45 1st eq.
tan (a-b)=tan 30
a-b=30 2nd eq.
add 1st and 2nd eq.
2a=75
a=75/2
a=37.5
put the value of a in 1st eq.
a+b=45
37.5+b=45
b=45-37.5
b=7.5

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