Question

Помогите с тригонометрией, пожалуйста. Найдите A(α)= , если .

Answer 1

Воспользуемся тригонометрическими тождествами:
$\frac{sin4a+(sin10a-sin6a)}{cos2a+(1-2sin^24a)}= \frac{2sin2acos2a+2sin2acos8a}{cos2a+cos8a}= \frac{2sin2a(cos2a+cos8a)}{cos2a+cos8a}= \\=2sin2a=4sina*cosa$
теперь возведем обе части в квадрат выражение $sina-cosa=m$
$m^2=(sina-cosa)^2=sin^2a-2sina*cosa+cos^2a= \\ =(sin^2a+cos^2a)-2sina*cosa=1-2sina*cosa \\ 2sina*cosa=1-m^2$
получается, что $A(a)=4sina*cosa=2*2sina*cosa=2(1-m^2)$

Answer 2

Trigonometric Function Calculation

To find A(α), we need more specific information or an equation to work with. However, I can provide some general information about trigonometric functions based on the search results.

Trigonometric functions are mathematical functions of an angle. They relate the angles of a triangle to the lengths of its sides. The primary trigonometric functions are sine, cosine, and tangent, often denoted as sin, cos, and tan respectively. Other related functions include cosecant, secant, and cotangent, denoted as csc, sec, and cot.

The relationship between these functions can be expressed in various trigonometric identities and equations. For example, one of the equations found in the search results is ctg a, 3 ctg a+4 sin a - cos a =12.

If you have a specific equation or problem related to trigonometric functions, please provide more details so that I can assist you further.