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Sunny_sXe [5.5K]
3 years ago
6

How do you write the expression as an angle sin42cos17-cos42sin17

Mathematics
1 answer:
kap26 [50]3 years ago
8 0
Sin(a+b)=sin(a)cos(b)+cos(a)sin(b).
Let a=42 and b=17 so sin(42+17)=sin59.
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Answer:

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Step-by-step explanation:

So we have the limit:

\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}

Let's remove the fractions in the denominator by multiplying both layers by (6+x)(6). So:

\lim_{x \to 0} \frac{\frac{1}{6+x}-\frac{1}{6}}{x}\cdot (\frac{(6+x)(6)}{(6+x)(6)})

Distribute:

=\lim_{x \to 0} \frac{(6)-(6+x)}{x(6+x)(6)}

Simplify the numerator:

=\lim_{x \to 0} \frac{6-6-x}{x(6+x)(6)}\\=\lim_{x \to 0} \frac{-x}{x(6+x)(6)}

Both the numerator and the denominator have an x. Cancel:

=\lim_{x \to 0} \frac{-1}{(6+x)(6)}

Direct substitution:

= \frac{-1}{(6+0)(6)}

Simplify:

=-1/36

And that's our answer.

And we're done!

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