Tan A = xsinB/1-xcosB and Tan B = ysinA/1-ysinA then sinA/sinB = ?

Asked by  | 23rd Aug, 2012, 09:55: AM

Expert Answer:

tan A = x sin B/ 1- x cosB
sin A / cos A = x sin B/ 1- x cosB
cos A / sinA = 1/x sinB - cosB/sinB
cos A / sinA + cosB/sinB = 1/x sinB           (1)
 
Similarly, from the second equality tan B = ysinA/1-ysinA, we get,
cos B / sinB + cosA/sinA = 1/y sinA           (2)
 
From (1) and (2), we get,
1/x sinB = 1/y sinA
Hence, sinA/ sinB = x/y

Answered by  | 23rd Aug, 2012, 10:30: AM

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