Question

If cosec(a-b)=2, cot( a+b)=1/√3, 0<(a+b)<90°,a>b, then find a&b

Answer 1

Answer: a= 45° and b=15°.

Answer 2

Cosec ( A - B ) = 2

And

Cot ( A + B ) = 1/√3

Se an write these equations As :

Cosec ( A - B ) = Cosec 30 ( As we know Cosec 30 = 2 )

So,

A - B = 30 --------------------- ( 1 )

And

Cot ( A + B ) = Cot 60 ( As we know Cot 60 = 1÷√3 )

So,

A + B = 60 ---------------------- ( 2 )

Now we add equation 1 and 2 and get

2A = 90​

A = 45​ ( Substitute that value in equation 2 and get )

45​ + B = 60

B = 15​

SO,

A = 45​ And B = 15