Sec A = Cosec B = 15/7, then find the value of A+B.

Asked by  | 20th Aug, 2011, 01:58: AM

Expert Answer:

secA = Cosec B = 15/7
So,   cos A =  sin B  = 7/15
 
sin A = { 1 - cos2 A }1/2 = { 1 - (15/7)2} 1/2 =   ?176 / 15
cos B = {  1 - sin2 B } 1/2 = { 1 - (15/7)2} 1/2 =   ?176 / 15
Now, sin ( A + B ) = sin A cos B + cos A sin B
                         = ?176 / 15  . ?176 / 15  + 7/15 . 7/15
                         = 176/225 + 49 / 225
                         = 225/ 225 = 1
sin ( A+B) = 1 = sin 90o
A  + B  = 90o
Hence , toe correct answer is option (3)

Answered by  | 20th Aug, 2011, 04:34: PM

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