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

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 90^o

A  + B  = 90^o

Hence , toe correct answer is option (3)