Example

3(r+2s)=2t-4
a⋅(b-2)=3b
3(r+2s)=2t-4
a⋅(b-2)=3b

Question

$$\sin 30+ \cos x=1$$

Answer

x=sequence(2*PI*n+arccos(1-sin(30)),in(n,Z)),sequence(2*PI*n+2*PI-arccos(1-sin(30)),in(n,Z))

Solution


Subtract \(\sin{30}\) from both sides.
\[\cos{x}=1-\sin{30}\]
Ask: What values of \(x\) will make \(\cos{x}\) equal \(1-\sin{30}\)?
\[x=\cos^{-1}{(1-\sin{30})},2\pi -\cos^{-1}{(1-\sin{30})}\]
Since cos is a periodic function, add the periodicity.
\[\begin{aligned}&x=2\pi n+\cos^{-1}{(1-\sin{30})},n \in Z\\&x=2\pi n+2\pi -\cos^{-1}{(1-\sin{30})},n \in Z\end{aligned}\]
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