Question

If tan (x)+cot(x)=2 then tan 2(x)+cot 2 (x)=?

Answer 1

Answer on Question #42095 – Math - Trigonometry

If $\tan(x) + \cot(x) = 2$ then $\tan 2(x) + \cot 2(x) = ?$

Solution:

We have

$$\tan(x) + \cot(x) = 2$$

Square both sides of equation:

$$(\tan(x) + \cot(x))^2 = 4$$ $$\tan^2(x) + 2 \tan(x) \cdot \cot(x) + \cot^2(x) = 4$$ $$\tan^2(x) + \cot^2(x) = 4 - 2 \tan(x) \cdot \cot(x)$$

Formula for the tangent:

$$\tan(x) = \frac{1}{\cot(x)}$$

Take into account (3) and rewrite (2):

$$\tan^2(x) + \cot^2(x) = 4 - 2 \tan(x) \cdot \frac{1}{\tan(x)} = 4 - 2 = 2$$

Answer: $\tan^2(x) + \cot^2(x) = 2$

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