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lawyer [7]
3 years ago
15

How do I establish this identity??

Mathematics
1 answer:
Aloiza [94]3 years ago
8 0
\frac{cosec\theta+cotan\theta} {sec\theta+tan\theta}=\frac{cosec\theta+cotan\theta} {sec\theta+tan\theta}\times\frac{cosec\theta-cotan\theta}{cosec\theta-cotan\theta}\times\frac{sec\theta-tan\theta} {sec\theta-tan\theta}

And use that,

\sec^2\theta-\tan^2\theta=1

cosec^2\theta-cotan^2\theta=1
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Warm-Up: Solve each equation for x.<br> 1. x + 5 = 15
eduard
X+5=15
-5 -5
X=10
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3 years ago
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What is -4/5 + 3/20 in simplest form
Helga [31]
-4/5 = -16/20, so the new expression is (-16/20)+(3/20)
then, -16 + 3 is -13, so the solution is -13/20
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After Ricardo received his allowance for the week, he went to the mall with some friends. He spent half of his allowance on a ne
ad-work [718]
Lets work backwards, he had $5 after it all, and spent $1.25 on a snack, so we add that to the remainder, which is $6.25. then he spent half of that on whatever stuff he likes, so add $6.25 and $6.25, which is $12.50
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3 years ago
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daniiel is currently 26 years older than his son. in 6 years he will be three times older than his son. how old are both of them
Molodets [167]

Answer:

Daniiel is 33 years old.

The son is 7 years old.

Step-by-step explanation:

x+26=3x

The x represents the son.

To solve for x:

-26=x-3x

-26=-2x

x=13

Since the father will be 3 times his son's age in six years we subtract 6.

x=7

This means the son is 7 years old as of right now. To find the father's age you do 7+26=33

7 0
3 years ago
et f(x) = x + |2x − 3|. Find all solutions to the equation f(x) = 12. (Enter your answers as a comma-separated list. If an answe
Alinara [238K]

Answer:

1. {5,-9}

2.{4}

3.{9/2}

Step-by-step explanation:

The equation f(x)=x+\lvert 2x-3 \rvert=12 can be solved as follows:

x+\lvert 2x-3 \rvert =12\,\,\,\text{(given equation)}

\lvert 2x-3 \rvert =12-x

2x-3=12-x\,\,\text{or}\,\,2x-3=-(12-x)

3x=15\,\,\text{or}\,\,\x=-9

Then, the solutions of the equation are x=5, x=-9.

Now, if g(x)=5x-3+\lvert x+4\rvert, we can solve the equation g(a)=4a+9 as follows:

5a-3+\lvert a+4 \rvert =4a+9

\lvert a+4\rvert =4a+9-5a+3

a+4 =-a+12\,\,\text{or}\,\,a+4=-(-a+12)

2a=8\,\,\text{or}\,\,4=12

So, the unique solution of this last equation is a=4

The last equation is h(x-1)=x-3, where h(x)=\lvert x \rvert -2x+5.. To solve this equation we can proceed as follows:

h(x-1)=x-3

\lvert x-1\rvert -2(x-1)+5=x-3

\lvert x-1 \rvert -2x+2+5=x-3

\lvert x-1\rvert =3x-10

x-1=3x-10\,\,\text{or}\,\,x-1=-(3x-10)

-2x=-9\,\,\text{or}\,\,4x=11

x=9/2\,\,\text{or}\,\,x=11/4

But, x=11/4 is not a solution of this equation. So the unique solution is x=9/2.

8 0
3 years ago
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