Question

(sina+tga):tga=1+cosa

Answer 1

$\frac{ \sin(a) + tg(a)}{tg(a)} = 1 + \cos(a)$

$\frac{ \sin(a) + tg(a)}{tg(a)} = \frac{ \sin(a) }{tg(a)} + \frac{tg(a)}{tg(a)} = \frac{ \sin(a) }{ \frac{ \sin(a) }{ \cos(a) } } + 1 = \\ \\ = \cos(a) + 1$


Тождество доказано

Answer 2

To solve the equation (sina + tga):tga = 1 + cosa, let's break it down step by step.

1. Recall the trigonometric identity: sin^2(a) + cos^2(a) = 1.

2. Divide both sides of the equation by tga:

   (sina + tga) / tga = (1 + cosa) / tga.

3. Simplify the left side of the equation:

   sina / tga + 1 = (1 + cosa) / tga.

4. Recall the trigonometric identity: sin(a) / cos(a) = tga(a). Rewrite the left side of the equation using this identity:

   tga(a) + 1 = (1 + cosa) / tga.

5. Multiply both sides of the equation by tga:

   tga(a) * tga + tga = 1 + cosa.

6. Distribute tga(a) on the left side of the equation:

   tga^2(a) + tga = 1 + cosa.

7. Recall the trigonometric identity: 1 + tga^2(a) = sec^2(a). Rewrite the equation using this identity:

   sec^2(a) - 1 = 1 + cosa.

8. Rearrange the terms:

   sec^2(a) - cosa - 2 = 0.

At this point, we have transformed the equation into a quadratic equation in terms of sec(a). To solve this equation further, we need additional information or constraints to determine the exact values of sec(a) or the angle 'a'. Without additional information, it is not possible to find a unique solution for this equation.