Find the angles at which $sin(heta)=cos(heta)$

To find the angles where $\sin (\theta )=\cos (\theta )$, we know that:

$\sin (\theta )=\cos (\theta )$

Dividing both sides by $\cos (\theta )$, we get:

$\tan (\theta )=1$

Thus, $\theta$ must be an angle where the tangent is 1. We know that $\tan (\theta )=1$ at:

$\theta =\frac{\pi }{4}+n\pi$

where $n$ is any integer. So, the angles are:

$\theta =\frac{\pi }{4},\frac{5\pi }{4},\frac{9\pi }{4},\dots$

To solve for $heta$ in $sin(heta)=cos(heta)$:

$sin(heta)=cos(heta)$

Divide by $cos(heta)$ to get:

$an(heta)=1$

This happens at:

$heta=fracpi4+npi$

for integer $n$. Therefore, the angles are:

$heta=fracpi4,frac5pi4,frac9pi4,\dots$

We need to find angles $heta$ where $sin(heta)=cos(heta)$:

$an(heta)=1$

This occurs at:

$heta=fracpi4+npi$

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