If sin⁡Asin⁡B=32 and cos⁡Acos⁡B=52,0

Given that,2sin⁡A=3sin⁡B⇒25sin⁡A=15sin⁡B----iand  2cos⁡A=5cos⁡B⇒23cos⁡A=15cos⁡B----iiOn squaring and adding Eqs. (i) and (ii), we get20sin2⁡A+12cos2⁡A=15⇒8sin2⁡A=3⇒sin2⁡A=38⇒cos2⁡A=58∴sin2⁡Acos2⁡A=35⇒tan⁡A=35