Question

Proove Tan70°=Tan20° +2Tan50°
Plz solve on a sheet and send a photo with steps

Answer 1

Equation (1): 

                      Tan 70

                   = Tan(50 + 20)  

We know that Tan(A + B) = Tan A + Tan B/1 - Tan A Tan B

$Tan 70 = \frac{Tan 50 + Tan 20}{1 - Tan 50 Tan 20}$

$Tan 70 * (1 - Tan 50*Tan 20) = Tan 50 + Tan 20$

Tan 70 - Tan 70 Tan 50 Tan 20 = Tan 50 + Tan 20

Tan 70 = Tan 50 + Tan 20 + Tan 70 Tan 50 Tan 20   ----- (1)


Equation (2):

Tan 70 = Tan(90 - 20)

            = Cot 20   ------ (2)


Substitute (2) in (1), we get

Tan 70 = Tan 50 + Tan 20 + cot 20 Tan 50 Tan 20

            = Tan 50 + Tan 20 + 1/tan 20 Tan 50 Tan 20(We know that Cot A = 1/tanA)

           = Tan 50 + Tan 20 + Tan 50

           = Tan 20 + 2 Tan 50.


LHS = RHS.


Hope this helps!

Answer 2

hey !!!

Tan70° =Tan( 50° +20° )

•°• Tan (A +B ) =TanA+ TanB / 1- TanA×TanB ( by using this formula), we can write

Tan70° =Tan50° +Tan20° /1-Tan50°×Tan20°

Tan70° - Tan70° ×Tan50°×Tan20° =Tan50° + Tan20° (By using cross multiplication rule )

Tan70° =Tan70°×Tan50° ×Tan20° +Tan50° +Tan20°

Tan70° = Tan(90°- 20° ) ×Tan50° ×Tan20°+ Tan50° +Tan20°

Tan70° =Cot20° ×Tan50° ×Tan20° +Tan50° +Tan20°

Tan70° = Tan50° +Tan50° +Tan20°

Tan70° =2Tan50° +Tan20°

Tan70° = Tan20° +2Tan50°

Prooved here ...

Hope it helps you!!

#Rajukumar111