Question

If cosec(A-B)=2, cot (A+B)=1/√3, 0°<(A+B)<90°,A>B, then find A and B.

Answer 1

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​

LIKE IF SATISFIED