Question

prove that :
(1+tan24)(1+tan21)(1+tan23)(1+tan22)=4​

Answer 1

[(1+ tan 24°)(1+ tan 21°)] [(1+ tan 23°)(1+ tan 22°) ][1+tan24+tan21+tan24tan21] [1+tan23+tan22+tan23tan22].......(1)tan(45)=1=tan(24+21) = tan(23+22)tan(A+B) = (tanA+tanB)/(1-tanAtanB)tan(24+21) = (tan24+tan21)/(1-tan24tan21)1*(1-tan24tan21)=tan24+tan211=tan24+tan21+tan24tan21....

(2)similarly, tan23+tan22+tan23tan22=1......

(3)substituting equation 2 & 3 in equation 1[1+1] [1+1]=4

Answer 2

Answer:

(1+ tan 24°)(1+ tan 21°)] [(1+ tan 23°)(1+ tan 22°) ][1+tan24+tan21+tan24tan21] [1+tan23+tan22+tan23tan22].......(1)tan(45)=1=tan(24+21) = tan(23+22)tan(A+B) = (tanA+tanB)/(1-tanAtanB)tan(24+21) = (tan24+tan21)/(1-tan24tan21)1*(1-tan24tan21)=tan24+tan211=tan24+tan21+tan24tan21....(2)similarly, tan23+tan22+tan23tan22=1......(3)substituting equation 2 & 3 in equation 1[1+1] [1+1]=4