1) 2 sinx cosx + 5 cos^2 x = 4 2)sin2x - 3cos^3 x = 4

Предыдущий
вопрос Следующий
вопрос

1) To simplify the given equation, we can use trigonometric identities. Let's start by using the double angle identity for sin(2x):

sin(2x) = 2sin(x)cos(x)

Now, let's replace sin(2x) in the equation with this identity:

2(2sin(x)cos(x)) + 5cos^2(x) =
4sin(x)cos(x) + 5cos^2(x) = 4

Now, we can factor out cos(x) from the first term:

cos(x)(4sin(x) + 5cos(x)) = 4

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

cos(x)(4cos(π/2 - x) + 5cos(x)) =
4cos(π/2 - x)cos(x) + 5cos^2(x) =
4sin(x)cos(x) + 5cos^2(x) = 4

So, the equation simplifies to 4sin(x)cos(x) + 5cos^2(x) = 4.

2) To simplify the given equation, let's start by using the Pythagorean identity:

sin^2(x) + cos^2(x) = 1

Now, let's rewrite sin^2(x) as 1 - cos^2(x) in the given equation:

1 - cos^2(x) - 3cos^3(x) = 4

Rearranging terms, we get:

-3cos^3(x) - cos^2(x) = 3

This is the simplified form of the second equation given.