Question

tan 70° = tan 20° + 2 tan 50°​

Answer 1

"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−tanb1+tanatanb

tan50=tan(70−20)=tan70−tan201+tan70tan20=tan70−tan201+1

2tan50=tan70−tan20

tan70=tan20+2tan50

"

Answer 2

Answer:

Tan70°​ = Tan20°​ + 2Tan 50°​

Proved!

Step-by-step explanation:

Correct Question:

Prove that : tan 70° = tan 20° + 2 tan 50°​

Solution:

We know that,

According to Trigonometric identity,

$\sf =.tan70=tan(20+50)\\\\\ =>tan70=(tan20+tan50)/1-tan20tan50\\\\\ =>tan70-tan20tan50tan70=tan20+tan50\\\\\ =>Also tan70tan20=tan70cot70=1\\\\\bigstar Hence,\\tan70-tan50=tan20+tan50\\\\\bf So,\sf tan70=tan20+2tan50 \quad\quad\bf(Proved)$