If a sin 2 ⁡ x + b cos 2 ⁡ x = c , b sin 2 ⁡ y + a cos 2 ⁡ y = d and a tan ⁡ x = b tan ⁡ y , then a 2 b 2 is equal to (Here a , b , c and d are distinct)

Step-by-step solution

Dividing the given equations by cos 2 ⁡ x & cos 2 ⁡ y respectively. We get, tan 2 x = c − b a − c and tan 2 y = d − a b − d ⇒ a 2 b 2 = tan 2 y tan 2 x = ( a − d ) ( c − a ) ( b − c ) ( d − b )