Respuesta :
Using trigonometric relations, it is found that:
[tex]\sin{\alpha}\cos{\alpha} = 0.22[/tex]
We are given that:
[tex]\sin{\alpha} + \cos{\alpha} = 1.2[/tex]
Hence:
[tex]\sin{\alpha} = 1.2 - \cos{\alpha}[/tex]
The basic relation is:
[tex]\sin^{2}{\alpha} + \cos^{2}{\alpha} = 1[/tex]
Hence:
[tex](1.2 - \cos{\alpha})^2 + \cos^{2}{\alpha} = 1[/tex]
[tex]2\cos^{2}{\alpha} - 2.4\cos^{\alpha} + 0.44 = 0[/tex]
Which is a quadratic equation, with coefficients [tex]a = 2, b = -2.4, c = 0.44[/tex].
Using a quadratic equation calculator, and considering that the cosine has to assume a value between 0 and 1, it is found that the solutions are:
[tex]\cos{\alpha} = 0.9742, \cos{\alpha} = 0.2258[/tex]
Since [tex]\sin{\alpha} = 1.2 - \cos{\alpha}[/tex], there are two solution pairs:
[tex](\sin{\alpha}, \cos{\alpha}) = (0.9742, 0.2258)[/tex]
[tex](\sin{\alpha}, \cos{\alpha}) = (0.2258, 0.9742)[/tex]
They result in the same multiplication result, hence:
[tex]\sin{\alpha}\cos{\alpha} = 0.9742(0.2258) = 0.22[/tex]
To learn more about trigonometric relations, you can take a look at https://brainly.com/question/24680641
