Question

6cos2x+5cos(п/2 -x)=7

Answer 1

Ответ:

x ⊄ R

Объяснение:

6cos(2x)+5cos(п/2-x)=7

6(1-2sin(x)2)+5sin(x)=7

6-12sin(x)2+5sin(x)=7

6-12sin(x)2+5sin(x)-7=0

-1-12sin(x)2+5sin(x)=0

-1-12t2+5t=0

t ⊄ R

X ⊄ R

Answer 2

To solve the equation 6cos(2x) + 5cos(π/2 - x) = 7, we'll first simplify the expression and then find the solutions for x.

Using the trigonometric identity cos(π/2 - x) = sin(x), we can rewrite the equation as:

6cos(2x) + 5sin(x) = 7

Next, let's focus on the term involving sine. We can express sine in terms of cosine using the identity sin(x) = cos(π/2 - x). So, we have:

6cos(2x) + 5cos(π/2 - x) = 7

Now, we'll use another trigonometric identity, cos(π/2 - x) = sin(x), to rewrite the equation again:

6cos(2x) + 5sin(x) = 7

We now have a trigonometric equation involving cosine and sine terms. To solve this equation, we'll need to use trigonometric identities and techniques.

Let's simplify further:

6cos(2x) + 5sin(x) = 7

Using the double-angle formula for cosine, cos(2x) = 2cos^2(x) - 1, we can substitute it into the equation:

6(2cos^2(x) - 1) + 5sin(x) = 7

Rearranging the terms:

12cos^2(x) + 5sin(x) - 6 = 7

12cos^2(x) + 5sin(x) = 13

Now, we have a trigonometric equation involving both cosine and sine terms. Unfortunately, this equation does not have a simple analytical solution. It requires numerical methods or graphing techniques to approximate the solutions.

You can use numerical methods like Newton's method or the bisection method to approximate the values of x that satisfy the equation. Alternatively, you can plot the graph of the equation and visually determine the approximate solutions.

Please note that due to the complexity of the equation, the solutions may not have simple closed-form expressions.