Example

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

Question

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

Answer

[Infinite Solutions]

Solution


Expand.
\[2\sin{x}\cos{x}+1-1=2\sin{x}\cos{x}\]
Simplify  \(2\sin{x}\cos{x}+1-1\)  to  \(2\sin{x}\cos{x}\).
\[2\sin{x}\cos{x}=2\sin{x}\cos{x}\]
Since both sides equal, there are infinitely many solutions.
Infinitely Many Solutions
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