Question

Sinx+sin(п+x) - cos(п/2+x)=1​

Answer 1

sin(x)+sin(п+x)-cos(п/2+x)=1

sin(x)-sin(x)-(-sin(x))=1

sin(x)=1

x=п/2+2kп , k€z

Answer 2

To solve the trigonometric equation $\sin(x) + \sin(\pi + x) - \cos\left(\frac{\pi}{2} + x\right) = 1$, we can use the properties of trigonometric functions and identities to simplify and solve for $x$.

Let's break down the equation step by step:

1. Recall that $\sin(\pi + x) = -\sin(x)$ and $\cos\left(\frac{\pi}{2} + x\right) = -\sin(x)$.
2. Substitute these values into the equation: $\sin(x) - \sin(x) + \sin(x) = 1$
3. Simplify the equation: $\sin(x) = 1$
4. Since the range of the sine function is $[-1, 1]$, there are no real solutions for $x$ that satisfy this equation.

So, the equation $\sin(x) + \sin(\pi + x) - \cos\left(\frac{\pi}{2} + x\right) = 1$ has no real solutions.