Solve equations using the trigonometric identities - High school Algebra II Exercises

Solve the following equations.

\cos^2\left(x\right)=\sin^2\left(x\right)

x = \dfrac{\pi}{4}\left(2n + 1\right), \ n \in \mathbb{Z}

x = \pi\left(2n + 1\right), \ n \in \mathbb{Z}

x = \dfrac{n\pi}{2}, \ n \in \mathbb{Z}

x = \dfrac{\pi}{2}\left(2n + 1\right), \ n \in \mathbb{Z}

\sin\left(2x\right)+\sin^{2}\left(x\right)=\cos^{2}\left(x\right)

x = \dfrac{\pi}{8} + \dfrac{n\pi}{2}, \ n \in \mathbb{Z}

x = \dfrac{\pi}{4} + n\pi, \ n \in \mathbb{Z}

x = \dfrac{\pi}{4} + 2n\pi, \ n \in \mathbb{Z}

x = \dfrac{\pi}{8} + n\pi, \ n \in \mathbb{Z}

\sqrt{3}\cos\left(x\right)+\sin\left(x\right)=2

x=\dfrac{\pi}{6}+{2}n\pi,\ n \in \mathbb{Z}

x=\dfrac{5\pi}{6}+{2}n\pi, \ n \in \mathbb{Z}

x=\dfrac{\pi}{2}+{2}n\pi, \ n \in \mathbb{Z}

x=-\dfrac{\pi}{3}+{2}n\pi, \ n \in \mathbb{Z}

\cos\left(x\right)\cos\left(\dfrac{\pi}{5}\right)=\sin\left(x\right)\sin\left(\dfrac{\pi}{5}\right)

x=\dfrac{3\pi}{10}+n\pi, \ n \in \mathbb{Z}

x=\dfrac{3\pi}{10}+2n\pi,\ n \in \mathbb{Z}

x=\dfrac{7\pi}{10}+n\pi, \ n \in \mathbb{Z}

x=\dfrac{7\pi}{10}+2n\pi,\ n \in \mathbb{Z}

\sin\left(x-\dfrac{\pi}{4}\right)=\sqrt{3}\cos\left(x-\dfrac{\pi}{4}\right)

x=\dfrac{7\pi}{12}+n\pi, \ n \in \mathbb{Z}

x=\dfrac{\pi}{12}+n\pi, \ n \in \mathbb{Z}

x=\dfrac{7\pi}{12}-n\pi, \ n \in \mathbb{Z}

x=\dfrac{\pi}{12}-n\pi, \ n \in \mathbb{Z}

\dfrac{1-\tan^{2}\left(x\right)}{1+\tan^{2}\left(x\right)}=1

x=n\pi,\ n \in \mathbb{Z}\\

x=2n\pi, \ n \in \mathbb{Z}\\

x=\dfrac{\pi}{4}+{2}n\pi, \ n \in \mathbb{Z}\\

x=\dfrac{\pi}{4}+n\pi, \ n \in \mathbb{Z}\\

\sin^{2}\left(x\right)+\cos^{2}\left(x\right)-2\sin\left(x\right)+1=0

x=\dfrac{\pi}{2}+{2}n\pi, \ n \in \mathbb{Z}

x=\dfrac{\pi}{2}+n\pi, \ n \in \mathbb{Z}

x=\dfrac{\pi}{2}-{2}n\pi,\ n \in \mathbb{Z}

x=\dfrac{\pi}{2}-n\pi, \ n \in \mathbb{Z}