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4 years ago

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Mathematics

1 answer:

My name is Ann [436]4 years ago

7 0

Answer:

step 1

Step-by-step explanation:

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Sin(A+B) sin(A-B) /sin^A Cos^B=1-cot^A Tan^B

telo118 [61]

In order to prove

$\dfrac{\sin(x+y)\sin(x-y)}{\sin^2(x)\cos^2(x)}=1-\cot^2(x)\tan^2(y)$

Let's write both sides in terms of $\sin(x),\ \sin^2(x),\ \cos(x),\ \cos^2(x)$ only.

Let's start with the left hand side: we can use the formula for sum and subtraction of the sine to write

$\sin(x+y)=\cos(y)\sin(x)+\cos(x)\sin(y)$

and

$\sin(x-y)=\cos(y)\sin(x)-\cos(x)\sin(y)$

So, their multiplication is

$\sin(x+y)\sin(x-y)=(\cos(y)\sin(x))^2-(\cos(x)\sin(y))^2\\=\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)$

So, the left hand side simplifies to

$\dfrac{\cos^2(y)\sin^2(x)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now, on with the right hand side. We have

$1-\cot^2(x)\tan^2(y)=1-\dfrac{\cos^2(x)}{\sin^2(x)}\cdot\dfrac{\sin^2(y)}{\cos^2(y)} = 1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

Now simply make this expression one fraction:

$1-\dfrac{\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}=\dfrac{\sin^2(x)\cos^2(y)-\cos^2(x)\sin^2(y)}{\sin^2(x)\cos^2(y)}$

And as you can see, the two sides are equal.

6 0

4 years ago

Determine the equation of the linear function that generates the following table of values.

Mashutka [201]

Answer:

y = -19x + 14

Step-by-step explanation:

For each increase of x by 1, y decreases by 19, giving us -19x. When x = 0, y = 14, therefore, y = -19x + 14

5 0

2 years ago

Is this true or false? 0 < -2 Answer fast pls

Feliz [49]

Answer:

False

Explanation:

It's actually 0 > -2

5 0

3 years ago

What’s quadratic equation

faltersainse [42]

Answer:

In algebra, a quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as ax^2+bx+c-0 where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a .0, then the equation is linear, not quadratic, as there is no ax^2 term. The numbers a, b, and c are the coefficients of the equation and may be distinguished by calling them, respectively, the quadratic coefficient, the linear coefficient and the constant or free term.

Step-by-step explanation:

Good Question I just had a class about it 10 minutes ago such a coincidence! :)

3 0

3 years ago

Read 2 more answers

Help me ill give 100 pts

hjlf

Answer:

Small Pizza = 1 . Large Pizza = 5.

Step-by-step explanation:

5 x 4 = 20 then just add 3 and you'll find how much both pizzas can feed the team. Hope this helps

5 0

3 years ago

Read 2 more answers