Question

tan(55+x)=cos(55-x)

Answer 1

Answer on Question # 41720 – Math – Trigonometry

$$\tan (55 + x) = \cos (55 - x)$$

Solution:

Co-Function Identities:

$$\sin \alpha = \cos (90{}^\circ - \alpha)$$ $$\cos \beta = \sin (90{}^\circ - \beta)$$ $$\cos (55{}^\circ - x) = \sin (90{}^\circ - (55{}^\circ - x)) = \sin (35{}^\circ + x)$$

Formula for the tangent:

$$\begin{array}{l} \tan (55{}^\circ + x) = \frac{\sin (55{}^\circ + x)}{\cos (55{}^\circ + x)} = \frac{\cos (90{}^\circ - (55{}^\circ + x))}{\sin (90{}^\circ - (55{}^\circ + x))} = \\ = \frac{\cos (35{}^\circ - x)}{\sin (35{}^\circ - x)} = \cot (35{}^\circ - x) \end{array}$$$$x \approx 2.(-0.839843 + 3.14159\,n),\ n \in \mathbb{Z}$$ $$x \approx 2(\pi n - 1.177),\ n \in \mathbb{Z}$$

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