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Lady bird [3.3K]
3 years ago
14

Root 3 cosec140° - sec140°=4prove that​

Mathematics
1 answer:
Lorico [155]3 years ago
3 0

Answer:

Step-by-step explanation:

We are to show that \sqrt{3} cosec140^{0} - sec140^{0} = 4\\

<u>Proof:</u>

From trigonometry identity;

cosec \theta = \frac{1}{sin\theta} \\sec\theta = \frac{1}{cos\theta}

\sqrt{3} cosec140^{0} - sec140^{0} \\= \frac{\sqrt{3} }{sin140} - \frac{1}{cos140} \\= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\

From trigonometry, 2sinAcosA = Sin2A

= \frac{\sqrt{3}cos140-sin140 }{sin140cos140} \\\\=  \frac{\sqrt{3}cos140-sin140 }{sin280/2}\\=  \frac{4(\sqrt{3}/2cos140-1/2sin140) }{2sin280}\\\\= \frac{4(\sqrt{3}/2cos140-1/2sin140) }{sin280}\\since sin420 = \sqrt{3}/2 \ and \ cos420 = 1/2  \\ then\\\frac{4(sin420cos140-cos420sin140) }{sin280}

Also note that sin(B-C) = sinBcosC - cosBsinC

sin420cos140 - cos420sin140 = sin(420-140)

The resulting equation becomes;

\frac{4(sin(420-140)) }{sin280}

= \frac{4sin280}{sin280}\\ = 4 \ Proved!

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Answer: \tan^2 t

Step-by-step explanation:

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2 years ago
Kyle drew three line segments with lengths: 2/4 inch 2/3inch, and 2/6 inch list the fractions in order from least to greatest
Sati [7]
----------------------------------------------------------------
Method 1
 ----------------------------------------------------------------
Since the numerators are the same, the smaller the denominators, the greater the fraction is.

Arranging from the least to the greatest
\dfrac{2}{6} \ , \ \dfrac{2}{4} \ , \ \dfrac{2}{3}


----------------------------------------------------------------
Method 2
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Lets change all to the same denominators 

\dfrac{2}{4}  =  \dfrac{2 \times 3}{4 \times 3}  =  \dfrac{6}{12}

\dfrac{2}{3}  =  \dfrac{2 \times 4}{3 \times 4}  =  \dfrac{8}{12}

\dfrac{2}{6}  =  \dfrac{2 \times 2}{6 \times 2}  =  \dfrac{4}{12}

Now that all the denominators are the same, we can arrange the fractions by comparing the numerators. The bigger the numerators, the greater the fraction.

Arranging from the least to the greatest
\dfrac{2}{6} \  , \   \dfrac{2}{4}  \ , \   \dfrac{2}{3}
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Substitute these values in the combined variation
zysi [14]

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G:6.67 x 10^ -11 N m2/kg2

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HELP? can anyone help? I’ll give Brainly the answer is not 3,240... thank you!
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9514 1404 393

Answer:

  $3144

Step-by-step explanation:

The tax due on $60,000 is ...

  $60,000 × 5.4% - $96 = $3144 . . . tax due

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The detailed calculation is described at brainly.com/question/23711444. The only difference is the value used in the highest bracket, $60,000 instead of $50,000. This adds $540 to the tax that would be due for $50,000.

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A sum of $900 is shared among Nas, Sam and Kristine in the ratio p: 5: 7. If Nas receives $120, what is the value of p?​
weqwewe [10]

Answer:

p+5+7=p+12

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90p-12p=144

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