Question

if A+B=45 then tanAtanB =?​

Answer 1

Answer:tan (A+B) = [(tan A + tan B) / (1 - tan(A)tan(B))]  

given that A+B = 45, we can rewrite the above equation as:  

tan45 = [(tanA + tanB) /(1- tanAtanB)]  

which implies that 1 = [(tanA + tanB) / (1 - tanAtanB)]  

this implies that 1 - tanAtanB = tanA + tanB  

this also implies that tanAtanB + tanA + tanB = 1  

by adding 1 both sides we get: tanAtanB +tanA + tanB +1 = 2  

we can then split the Left Hand Side of the equation into two parts:  

(tanAtanB +tanA) + (tanB +1) = 2  

we then factorise the first part by considering the term 'tanA' to get:  

tanA(tanB + 1) + (tanB + 1) = 2  

After this we can factorise the left hand side further by considering the term 'tanB + 1' to get: (tanB + 1) (tanA +1) = 2  

which implies that:  

(1 + tanA) (1 + tanB) = 2  

I hope this is clear enough.

Step-by-step explanation: