Answer :

Given: tan A = n tan B

Therefore,   


Thus,

Squaring both sides, we get,

cot2 B = n2/tan2 A ……(1)


Also, sin A = m sin B


Therefore, sin B = sin A/m


Thus, cosec B = m/sin A


cosec2 B = m2/sin2 A ……(2)


Now, subtract equation (2) from (1):


cosec2 B – cot2 B =


1 =


1 =


m2 – n2 cos2 A = sin2 A


m2 – n2 cos2 A = 1 – cos2 A


m2 – 1 = n2 cos2 A – cos2 A


(n2 – 1)cos2 A = m2 – 1


cos2 A = (m2 – 1)/(n2 – 1)


Hence, proved.

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