Question

Prove that tan70° = 2tan50° + tan20° . ​

Answer 1

Answer:

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your answer is here !

Explanation:

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

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A.A.

Answer 2

Answer:

To prove:-

• tan70° = 2tan50° + tan20°

Explanation:

$\tan(70 \degree) = \tan(20 \degree + 50 \degree) \\ \\ \sf \star \: using \: trigonometery \: identity\\ \\ \sf \tan(A+B) = \frac{\tan A + \tan B}{1 -\tan A \tan B } \\ \\ \sf \tan(20 \degree \: +50 \degree) = \frac{\tan 20 \degree + \tan 50 \degree}{1 -\tan 20 \degree\tan 50 \degree}$

Now cross multiplying the values

$\sf : \implies1 - tan20 \degree\: tan50\degree(tan20\degree tan50\degree) = tan20\degree+ tan50\degree \\ \\ \sf : \implies tan70\degree - tan20\degree. tan50\degree. tan70\degree =tan20\degree + tan50\degree \\ \\ \sf : \implies tan70\degree = tan70\degree \: tan50\degree \: tan20\degree+ tan20\degree+ tan50\degree \\ \\ \sf : \implies tan70\degree = cot20\degree \: tan50\degree tan20\degree+ tan20 \degree\: + tan50\degree</p><p> \\ \\ \sf Therefore,</p><p> \\ \\ \tt [tan70\degree=tan(90\degree-20\degree) = cot20\degree]</p><p> \\ \\\sf : \implies 2tan50\degree + tan20\degree$

Hence, #proved