Question

tan 35° + 2 tan 20º = tan x => x =​

Answer 1

Answer:

Step-by-step explanation:

20 = 55 - 35

∴ tan(20)=tan(55-35)

tan(20)=  

1+tan55+tan35

tan55−tan35

​  

  (∴tan(A+B)=  

1−tanA.tanB

tanA+tanB

​  

)

Now, 55+35=90

35 = 90 - 55

tan 35 = tan(90-55)

tan 35 = cot(55)    ∵tan(90−θ)=cotθ

Thus, tan 20 =  

1+tan55.cot55

tan55−tan35

​  

 

∴tan(20)×(1+1)=tan55−tan35           (∵tanθ.cotθ=1)

∴2tan20+tan35=tan55.