Question

Prove that:-Tan 70 = tan 20 + 2 tan 50

Answer 1

with reference to the attachment....

⏹Split tan 70 as tan(50+20)

✔️✔️so now use the formula:-------

⏹tan(A+B)=TanA+TanB÷1-TanATanB⏹

✔️✔️In the equation 2 use the formula where:-----

⏹Tan(90-A=cotA)⏹

✔️In the last equation i.e 3rd one use the formula :------

⏹cotA=1÷tanA⏹

Answer 2

Answer:

• According to the trigonometric identity,

tan70 = tan (20 + 50)

tan70= (tan20 + tan50) / 1-tan20 tan50

Tan70 - tan20 tan50 tan70= tan20 + tan50

Also tan70 tan20 = tan70 cot70 = 1

• Hence, it will change to following equation

tan70 - tan50 = tan20 + tan50

So tan70 = tan20 + 2tan50

• Complementary angles:

tan70=cot20

tan70tan20=cot20tan20=1

• Tangent difference angle formula:

tan(a−b)=tana−tanb 1+tana tanb

tan50=tan(70−20)=tan70−tan20 1+tan70 tan20=tan70−tan20 1+1

2tan50=tan70−tan20

tan70=tan20+2tan50