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Nookie1986 [14]
3 years ago
10

Q6 Q19.) Write the expression as the​ sine, cosine, or tangent of an angle. Then find the exact value of the expression.

Mathematics
1 answer:
Greeley [361]3 years ago
3 0
Using sin(A+B) = sinAcosB + cosAsinB

sin20cos40 + cos20sin40 = sin(20+40) = sin60degree

= \frac{ \sqrt{3}}{ 2}
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Prove the sum of two rational numbers is rational where a, b, c, and d are integers and b and d cannot be zero. Steps Reasons 1.
harkovskaia [24]

Answer:

\dfrac{ad+bc}{bd}

Step-by-step explanation:

Let \frac{a}{b} and \frac{c}{d} be two rational numbers, where b and d are not zero and a, b, c and d are integers.

1. Given:

\dfrac{a}{b}+\dfrac{c}{d}

2. Multiply to get a common denominator :

\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd}+\dfrac{cb}{db}

3. Simplify:

\dfrac{a}{b}+\dfrac{c}{d}=\dfrac{ad}{bd}+\dfrac{cb}{db}=\dfrac{ad+bc}{bd}

4. Since b\neq 0,\ d\neq 0, then bd\neq 0.

If a,b,c,d are integers, then bd, ad,bc, ad+bc are integers too. So the fraction

\dfrac{ad+bc}{bd}

is a rational number

6 0
3 years ago
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