Question

if sin t+cos t=1/5 then find tan t/2 is

Answer 1

Sin t + cost = 1/5 ⇒ 2tan(t/2)/ 1 + tan²(t/2) + 1 - tan²(t/2)/ 1 + tan²(t/2)= put tan (t/2) = mnow 2m + 1 - m² / 1 + m² = 1/5 ⇒10m + 5 - 5m² = 1+ m² ⇒ 6m² - 4 -10m = 03m² -5m - 2 = 0 ⇒ 3m² - 6m + m - 2 = 0⇒ (3m+1)(m-2)= 0 ⇒ tan (t/2) = -1/3 or 3

hope this will help !!