Question

Sin x + cos x =sinxcosx + 1

Answer 1

Sin(x)+cos(x)=sin(x)cos(x)+1
sin(x)+cos(x)-sin(x)cos(x)-1=0
sin(x)(-cos(x)+1)-1(-cos(x+1)=0
(sin(x)-1)(1-cos(x))=0
sin(x)=1 или сos(x)=1
x=(pi/2)+2*pi*n, n-целые числа
илт х=2*pi*k, k-целые числа
ответ:x=(pi/2)+2*pi*n; х=2*pi*k;
n,k-целые числа

Answer 2

To determine whether the given equation is true or false, we can use some trigonometric identities and basic algebraic manipulation. Let's start by breaking down the equation:

sin(x) + cos(x) = sin(x) * cos(x) + 1

First, let's try to simplify the right-hand side of the equation:

sin(x) * cos(x) + 1

We can use the trigonometric identity: sin(x) * cos(x) = (1/2) * sin(2x)

So the right-hand side becomes:

(1/2) * sin(2x) + 1

Now, the equation becomes:

sin(x) + cos(x) = (1/2) * sin(2x) + 1

Now, we need to use another trigonometric identity:

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

Substitute this back into the equation:

sin(x) + cos(x) = (1/2) * (2 * sin(x) * cos(x)) + 1

Now, simplify:

sin(x) + cos(x) = sin(x) * cos(x) + 1

At this point, we can see that the equation is the same on both sides:

sin(x) + cos(x) = sin(x) * cos(x) + 1

So, the given equation is true.