If someone spent 9/15 hour shopping and 4/5 cleaning, how much more time in hours was spent cleaning?

Mathematics

1 answer:

VARVARA [1.3K]3 years ago

3 0

Answer:

Step-by-step explanation:

4/5 - 9/15 =

12/15 - 9/15 =

3/15 reduces to 1/5

so he spent 1/5 of an hr more cleaning

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9. What is the tan(90-x)?

Aleonysh [2.5K]

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$\\ \sf\longmapsto x=53°$

$\\ \sf\longmapsto tan(90-x)$

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2 years ago

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Root 3 cosec140° - sec140°=4 prove that

Lorico [155]

Answer:

Step-by-step explanation:

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

Proof:

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

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