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3 years ago

If 2tanA=3tanB,then prove that tan(A-B)=sin2B/(5-cos2B) ...?

1 answer:

8 0

Tan ( A - B ) = ( tan A - tan B ) / ( 1 + tan A tan B )
tan A = 3 tan B/2
tan ( A - B ) = ((3 tan B/ 2)-tan B) / ( 1 + 3 tan² B/2)=
= (tan B/2) / ( 2 + 3 sin²B/cos²B )=
= (sin B / cos B) / (( 2cos² B+3sin²B)/cos²B)=
=( sin B cos B ) / ( 2 cos²B + 3 ( 1 - cos² B ) ) =
= (sin B cos B ) / ( 2 cos² B + 3 - 3 cos² B ) =
= ( sin 2 B ) / 2 ( 3 - cos² B ) =
= ( sin 2 B ) / ( 6 - cos² B )=
= ( sin 2 B ) / ( 5 + 1 - 2 cos² B )=
= ( sin 2 B ) / ( 5 + sin² B + cos ² B - 2 cos² B ) =
= ( sin 2 B ) / ( 5 - ( cos² B - sin² B ) ) =
= ( sin 2 B ) / ( 5 - cos 2 B ) - correct

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poizon [28]

Answer:

8x³ 24x²

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Step-by-step explanation:

When factoring quadratics, you need to multiply each term with the other term.

So In this case, in the first box, you must do 4x² times 2x, which gives you 8x³.

continue this process until you get the answer shown above.

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A bottle holds 8.2 ounces of disinfecting soap. Jesse used 0.2 of the soap in the bottle to clean the kitchen floor. How many ou

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3 years ago

The height of one solid limestone square pyramid is 21 m. A similar solid limestone square pyramid has a height of 30 m. The vol

Elina [12.6K]

Answer:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form is $\frac{7}{10}$

Part b) The ratio of the volume of the smaller pyramid to the larger pyramid is $\frac{343}{1,000}$

Part c) The volume of the smaller pyramid is $4,116\ m^{3}$

Step-by-step explanation:

Part a) The scale factor of the smaller pyramid to the larger pyramid in simplest form

we know that

If two figures are similar, then the ratio of its corresponding sides is equal and this ratio is called the scale factor

Let

z----> the scale factor

x----> the height of the smaller pyramid

y----> the height of the larger pyramid

$z=\frac{x}{y}$

substitute the values

$z=\frac{21}{30}$

Simplify

$z=\frac{7}{10}$ -----> scale factor in simplest form

Part b) Ratio of the volume of the smaller pyramid to the larger pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

substitute

$\frac{7}{10}^{3}=\frac{x}{y}$

Rewrite

$\frac{x}{y}=\frac{343}{1,000}$ -----> ratio of the volume of the smaller pyramid to the larger pyramid

Part c) The volume of the smaller pyramid

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x----> the volume of the smaller pyramid

y----> the volume of the larger pyramid

$z^{3}=\frac{x}{y}$

we have

$z=\frac{7}{10}$

$y=12,000\ m^{3}$

substitute the values and solve for x

$(\frac{7}{10})^{3}=\frac{x}{12,000}$

$x=\frac{343}{1,000}(12,000)=4,116\ m^{3}$

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3 years ago

Which of the following is equal to tan θ using coordinates on the unit circle? Question 18 options: A) x∕y B) y C) y∕x D) x

kramer

Answer:

Solution given

tan θ=opposite/adjacent=y/x is a required answer.

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blondinia [14]

Answer:

Step-by-step explanation:

Substitute x with -6:

2(-6)²-2

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2 years ago

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