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geniusboy [140]
3 years ago
14

Evaluate the following expression (2.3)-3(1,1)

Mathematics
2 answers:
inessss [21]3 years ago
5 0

Answer: (-1,0)

Step-by-step explanation:

i just took the quiz

uranmaximum [27]3 years ago
3 0

Answer:

<em><u>2</u></em><em><u>.</u></em><em><u>3</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>(</u></em><em><u> </u></em><em><u>3</u></em><em><u>,</u></em><em><u> </u></em><em><u>1</u></em><em><u>)</u></em><em><u> </u></em>

Step-by-step explanation:

1) Simplify  3 × (1, 1) 3 × (1, 1)  to  3× 1, 13 × 1,1.

<em>2</em><em>.</em><em>3</em><em> </em><em>-</em><em> </em><em>(</em><em> </em><em>3</em><em> </em><em>×</em><em> </em><em>1</em><em>,</em><em> </em><em>1</em><em> </em><em>)</em>

2) Simplify 3 × 1 to 3.

2.3 - ( 3, 1)

<em><u>Therefor</u></em><em><u>,</u></em><em><u> </u></em><em><u>the</u></em><em><u> </u></em><em><u>answer</u></em><em><u> </u></em><em><u>is</u></em><em><u> </u></em><em><u>2</u></em><em><u>.</u></em><em><u>3</u></em><em><u> </u></em><em><u>-</u></em><em><u> </u></em><em><u>(</u></em><em><u> </u></em><em><u>3</u></em><em><u>,</u></em><em><u> </u></em><em><u>1</u></em><em><u>)</u></em><em><u>.</u></em>

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2 tan 30°<br>II<br>1 + tan- 300​
shusha [124]

Question:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Answer:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

Step-by-step explanation:

Given

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}

Required

Simplify

In trigonometry:

tan(30^{\circ}) = \frac{1}{\sqrt{3}}

So, the expression becomes:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + (\frac{1}{\sqrt{3}})^2}

Simplify the denominator

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2 * \frac{1}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{1 + \frac{1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{3+1}{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\frac{2}{\sqrt{3}}}{ \frac{4}{3}}

Express the fraction as:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= \frac{2}{\sqrt 3} / \frac{4}{3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{2}{\sqrt 3} * \frac{3}{4}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{1}{\sqrt 3} * \frac{3}{2}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3}

Rationalize

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3}{2\sqrt 3} * \frac{\sqrt{3}}{\sqrt{3}}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{3\sqrt{3}}{2* 3}

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})} = \frac{\sqrt{3}}{2}

In trigonometry:

sin(60^{\circ}) =  \frac{\sqrt{3}}{2}

Hence:

\frac{2tan30^{\circ}}{1 + tan^2(30^{\circ})}= sin(60^{\circ})

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