Given the general identity tan X = , which equation relating the acute angles, A and C, of a right â†ABC is true? A. Tan A = B.

Question

3 years ago

8

Cos A = C. Sin C = D. Cos A = tan C E. Sin C =.

2 answers:

malfutka [58] · Answer 1 · 2022-08-25T15:45:24+03:00

The equation $\tan(A) = \frac{\sin(A)}{\sin(C)}$ relating the acute angles, A and C, of the right triangle ABC is true

The general identity is given as:

$\tan(x) = \frac{\sin(x)}{\cos(x)}$

The acute angles of the right triangles are given as A, and C.

So, we have:

$A + C = 90$

This also means that:

$\sin(A) = \cos(C)$

and

$\sin(C) = \cos(A)$

Substitute A for x in $\tan(x) = \frac{\sin(x)}{\cos(x)}$

$\tan(A) = \frac{\sin(A)}{\cos(A)}$

Substitute sin(C) for cos(A) in $\tan(A) = \frac{\sin(A)}{\cos(A)}$

$\tan(A) = \frac{\sin(A)}{\sin(C)}$

Hence, the equation $\tan(A) = \frac{\sin(A)}{\sin(C)}$ relating the acute angles, A and C, of the right triangle ABC is true