Question

SIN^2 X -SIN X COS X -2COS^2 X = a Где вы, знающие люди? ))

Answer 1

Sin²x - SinxCosx -2Cos²x = a*1
Sin²x - SinxCosx -2Cos²x = a*(Sin²x + Cos²x)
Sin²x - SinxCosx -2Cos²x = aSin²x + aCos²x 
Sin²x - SinxCosx -2Cos²x - aSin²x - aCos²x = 0
Sin²x(1 -a) -Cos²(1 +a) -  SinxCosx = 0 | : Сos²x ≠0
tg²x(1 - a) -tgx -(1 +a) = 0
tgx = y
y²(1 -a) - y -(1 +a) = 0
D = b² -4ac = 1 + 4*(1-a)(1+a)= 1 + 4 - 4a² = 5 -4a²
a) 5-4a² ≥ 0                      б) 5 - 4a² < 0
     4a²≤ 5                             нет решений.
       a² ≤ 5/4
-√5/2 ≤ a ≤ √5/2
у = (1 +- √(5-4а²))/2(1 - а)
tgx = (1 +-√(5 - 4a²)/(2(1 - a)      (учтём, что √5/2 ≤ a ≤ √5/2  и  а ≠ 1
х =  arctg (1 +-√(5 - 4a²)/(2(1 - a) ,  √5/2 ≤ a ≤ √5/2 и а ≠ 1

Answer 2

Solving the Equation SIN^2(X) - SIN(X)COS(X) - 2COS^2(X) = a

To solve the equation SIN^2(X) - SIN(X)COS(X) - 2COS^2(X) = a, we can use trigonometric identities to simplify and manipulate the equation.

First, let's start by using the trigonometric identity SIN^2(X) + COS^2(X) = 1. We can express COS^2(X) as 1 - SIN^2(X).

So, the equation becomes: SIN^2(X) - SIN(X)COS(X) - 2(1 - SIN^2(X)) = a

Simplify the equation: SIN^2(X) - SIN(X)COS(X) - 2 + 2SIN^2(X) = a 3SIN^2(X) - SIN(X)COS(X) - 2 = a

Now, we can use the trigonometric identity SIN(2X) = 2SIN(X)COS(X) to express SIN(X)COS(X) as 0.5SIN(2X).

The equation becomes: 3SIN^2(X) - 0.5SIN(2X) - 2 = a

This equation can be further manipulated based on the value of a or the specific values of X.

Let's continue the calculation based on the specific value of a or X if provided.

If you have a specific value for a or X, please provide it so we can continue solving the equation.