Question

If cosec(A+B)=-1and cot(A-B)=root3 find AandB

Answer 1

To find :- A and B

Since,
cosec(A+B)= -1

therefore, cosec(A+B) = -Cosec 90°

A+B= -90 ------(1)

and, cot(A-B)= root3

cot(A-B)= cot 30°

A-B= 30 -------(2)

from(1) an (2) we get,

A+B= -90
A-B= 30
(-) (+) (-)
______________
2B= -120

B= -60 --------(3)


therefore, putting the value of (3) in (1)

A+B= -90

A+(-60) = -90

A- 60= -90

A= -90+60

A= -30
therefore, A= -30 ; B= -60.

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