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3 years ago

1/sin30 - √3/cos10 =4 prove it?

Mathematics

1 answer:

Crank3 years ago

8 0

Step-by-step explanation:

1/sin10-√3/cos10

= (cos10 - √3sin10)/cos10sin10

multiplying 1/2 in denominator and numerator

= {(cos10/2) - (√3sin10/2)}/(cos10sin10/2)

= (cos60cos10 - sin60sin10)/(cos10sin10/2)

= cos(60 + 10)/(cos10sin10/2)

= cos70/(cos10sin10/2)

= 2cos70/cos10sin10

multiplying 2 on numerator and denominator

= 4cos70/2sin10cos10

=4cos70/sin20

=4cos70/cos70

= 4 proved

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Read 2 more answers

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In this case, the washer method seems to be easier and thus, it is the one I will use.

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For the washer method, we need to find the area function, which is given by:

$A=\pi\cdot [(\rm{outer\ radius)^2 -(\rm{inner\ radius)^2 ]$

By taking a look at the plot I attached, one can easily see that for a rotation around the y-axis the outer radius is given by the function $x=\sqrt{y}$ and the inner one by $x=y^2$ . Thus, the area function is:

$A(y)=\pi\cdot [(\sqrt{y} )^2-(y^2)^2]\\A(y)=\pi\cdot (y-y^4)$

Now we just need to integrate. The integration limits are easy to find by just solving the equation $\sqrt(y)=y^2$ , which has two solutions $y=0$ and $y=1$ . These are then, our integration limits.

$V=\pi\int_{0}^1 (y-y^4)dy\\ V=\pi (\int_{0}^1 ydy - \int_{0}^1 y^4dy)\\ V=\pi/2-\pi/5\\\boxed{V=3\pi/10}$

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4 years ago

1/sin30 - √3/cos10 =4 prove it?​

1/sin30 - √3/cos10 =4 prove it?