Question

cot(A+B)=1 , cosec(A-B) =2 then find A and B​

Answer 1

Answer:

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GIVEN:

$\cot(a + b) = 1 \\ \csc(a - b) = 2$

TO FIND :

FIND A AND B

PROOF :

$\cot(a + b) = 1 \\ \cot(a) + \cot(b) = 1 \:$

THEREFORE

$\csc(a - b) = 2 \\ \csc(a) - \csc(b) = 2 \\ \csc(a) = 2 + \csc(b)$

$\frac{1}{ \sin(a) } = 2 + \frac{1}{ \sin(b) } \\ \frac{1}{ \sin(a) } = \frac{2 \sin(b) }{ \sin(b) } \\ \frac{1}{ \sin(a) } = \sin(b)$

SO ;

$\frac{ \cos(a) }{ \sin(a) } + \frac{ \cos(b) }{ \sin(b) } = 1 \\ \frac{ \sin(b) \times \cos(a) + \cos(b) \times \sin(a) }{ { \sin(a + b) }^{2} } = 1$

HOPE THAT HELPS