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My name is Ann [436]
3 years ago
9

Find all solutions to the equation.

Mathematics
1 answer:
Bess [88]3 years ago
3 0

If the equation is

7\sin^2x-14\sin x+2=-5

then rewrite the equation as

7\sin^2x-14\sin x+7=0

Divide boths sides by 7:

\sin^2x-2\sin x+1=0

Since x^2-2x+1=(x-1)^2, we can factorize this as

(\sin x-1)^2=0

Now solve for <em>x </em>:

\sin x-1=0

\sin x=1

\implies\boxed{x=\dfrac\pi2+2n\pi}

where <em>n</em> is any integer.

If you meant sin(2<em>x</em>) instead, I'm not sure there's a simple way to get a solution...

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