Question

If tan (x+y)=root 3 and tan(x-y)=1/root 3 find the values of a nd y

Answer 1

HELLO DEAR,


tan(x+y)=√3

=> tan(x+y) = tan60°

=> x+y=60°----------(1)


--------------------- -------------------

tan(x-y)= 1/√3

=> tan(x-y )= tan30°

=>. x-y =30°----------(2)



from ---(1) and---(2)

x+y=60
x-y=30
_________
2x=90

x=90/2

=> X= 45°put In---(1)

we get,

x+y=60

=> 45+y=60

=> y=60-45

=> y=15° AND x=45°



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Answer 2

Tan(X+Y)=tan60

X+Y=60 eqn 1

Tan(X- Y) = Tan30

X-Y= 30 eqn 2

Elimination method

From eqn 1 and 2

X+Y= 60

X-Y=30

2 X = 90

X= 90/2

X= 45

Put the value of X in eqn 2

We get ,

X- Y = 30

45 - Y= 30

-Y= 30 -45

- y= -15

Y= 15

Si we get the value of X = 45 and Y = 15