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2 years ago

Prove this (sinx-tanx)(cosx-cotx)=(sinx-1)(cosx-1)

Mathematics

2 answers:

Ilya [14]2 years ago

6 0

(sinx−tanx)(cosx−cotx)

=(sinx−sinxcosx)(cosx−cosxsinx)

=sinx(1−1cosx)cosx(1−1sinx)

=sinx(cosxcosx−1cosx)cosx(sinxsinx−1sinx)

=sinxcosx(cosx−1)cosxsinx(sinx−1)

=(cosx−1)(sinx−1)

faltersainse [42]2 years ago

4 0

Distribute first
sinx cosx - sinx cotx - cosx tanx+tanx cotx
sinx cosx - sinx (cosx/sinx) - cosx (sinx/cosx) + tanx (cosx/sinx)
sinxcosx - cosx - sinx +1
and factor
cosx(sinx -1) -1(sinx - 1)
(sinx -1)(cosx-1)

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The law of cosines is a^2+b^2-2abcosC=c^2. Find the value of 2abcosC.

polet [3.4K]

2ab x cos (C) = 7 because

a^2 + b^2 - 2ab x cos(C) = c^2
2ab x cos(C) = a^2 + b^2 - c^2
2ab x cos(C) = 2^2 + 2^2 - 1^2
2ab x cos (C) = 7

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2 years ago

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Which quadratic equation is equivalent to (x2 – 1)2 – 11(x2 – 1) + 24 = 0? u2 – 11u + 24 = 0 where u = (x2 – 1) (u2)2 – 11(u2) +

Vinvika [58]

u2 – 11u + 24 = 0 where u = (x2 – 1) the first awnser, a.

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2 years ago

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Hannah and Corrine are playing a game by rolling two cubes, each numbered 1 through 6. If the sum of the numbers on the cubes is

Katarina [22]

Answer:

D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

Step-by-step explanation:

To get a sum of 7 by rolling two cubes, we need to get one of the combinations from the list below:

1 on the first cube, 6 on the second cube

6 on the first cube, 1 on the second cube

2 on the first cube, 5 on the second cube

5 on the first cube, 2 on the second cube

3 on the first cube, 4 on the second cube

4 on the first cube, 3 on the second cube

Therefore, the correct answer option is D. Corrine is not correct because Hannah also wins if 6 is on the first cube and 1 is on the second, if 5 is on the first cube and 2 is on the second, and if 4 is on the first cube and 3 is on the second.

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2 years ago

How many ounces of pure nickel must be added to 150 ounces of alloy 70% pure to make an alloy which is 85% pure?

galben [10]

Answer:

150 oz.

Step-by-step explanation:

There are already 150 ounces of alloy of nickel.

Of this 150 oz, 70% is pure i.e. nickel content = 150(0.7) = 105 oz

Now available is

Nickel Other metals

105 45

Let x oz of pure nickel is added.

Then new alloy will have 105+x oz nickel in total of 150+x oz.

Percentage pure = $\frac{105+x}{150+x} =85%$

Simplify to get

$\frac{105+x}{150+x} =\frac{85}{100} \\\\Cross multiply:\\85(150+x) =100(105+x)\\12750+85x =10500+100x\\100x-85x = 12750-10500\\15x = 2250\\x = 150$

Hence answer is 150 oz should be added.

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2 years ago

nadia was offered a job for selling ads cor a magazine. She must agree to one of the following paymen options. CHOICE A:$110 for

Fittoniya [83]

Let us say that:

x = is the number of ads that Nadia sold every week

P = payment or amount that she receives every week

So the equations we can formulate for choice A and B are:

choice A: P = 110 x

choice B: P = 150 + 85 x

The amount that she receives for A must be greater than she receives for choice B, so:

110 x > 150 + 85 x (inequality equation)

Calculate for x:

110 x – 85 x > 150

25 x > 150

x > 6

Therefore Nadia must sell more than 6 ads every week so that Choice A would be the better choice.

6 0

2 years ago