Question

Prove that :
Tan 70 - tan 50 - tan 20 =tan70×tan50×tan20​

Answer 1

Answer:

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Answer 2

Answer:

We know,

$\tan(a + b) = \frac{ \tan(a) + \tan(b) }{1 - \tan(a) \tan(b) }$

Now,

$\tan(70) = \tan(50 + 20) \\ = \frac{ \tan(50) + \tan(20) }{1 - \tan(50) \tan(20) }$

By cross multiplication,

$\tan(50) + \tan(20) = \tan(70) - \tan(70) \tan(50) \tan(20)$

$\tan(70) - \tan(50) - \tan(20) = \tan(70) \tan(50) \tan(20)$

[proved]

This is a problem of Trigonometry.

Some important Trigonometry formulas,

$sin(x) = \cos(\frac{\pi}{2} - x) \\ \tan(x) = \cot(\frac{\pi}{2} - x) \\ \sec(x) = \csc(\frac{\pi}{2} - x) \\ \cos(x) = \sin(\frac{\pi}{2} - x) \\ \cot(x) = \tan(\frac{\pi}{2} - x) \\ \csc(x) = \sec(\frac{\pi}{2} - x)$

know more about Trigonometry,

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