Question

If A + B + C = 180
and cos A = cob B cos C
Then prove,
i)tan A=tan B + tan C
ii)2cotBcotC=1​

Answer 1

Step-by-step explanation:

SOLUTION :

A + B + C = 180° (given)

=> B + C = 180° - A

=> sin(B + C) = sin(180° - A)

=> sinB . cosC + cosB . sinC = sinA

sinB . cosC + cosB . sinC sinA

=> --------------------------------------- -- -----------

cosA cosA

sinB . cosC cosB . sinC sinA

=> ------------------- + ------------------ -- -----------

cosA cosA cosA

sinB . cosC cosB . sinC sinA

=> ------------------- + ------------------ -- -----------

cosB . cosC cosB . cosC cosA

sinB . cosC cosB . sinC sinA

=> ------------------- + ------------------- -- -----------

cosB . cosC cosB . cosC cosA

sinB sinC sinA

=> ---------- + ---------- -- -----------

cosB cosC cosA

=> tanB + tanC = tanA

=> tanA = tanB + tanC

(Proved)