We have, 3sin‌(α−β)=5‌cos(α+β) ‌⇒3[sin‌α‌cos‌β−cos‌α‌s‌i‌n‌β] ‌‌‌=5[cos‌α‌cos‌β−sin‌αsin‌β] On dividing by cos‌α‌cos‌β, we get ‌3[tan‌α−tan‌β]=5(1−tan‌α‌tan‌β) ⇒3‌tan‌α−3‌tan‌β=5−5‌tan‌α‌tan‌β ⇒3‌tan‌α+5‌tan‌α‌tan‌β=5+3‌tan‌β ⇒tan‌α(3+5‌tan‌β)=5+3‌tan‌β ⇒tan‌α=‌