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3 years ago

Plz help me hurry plz Direct variation

Mathematics

1 answer:

Furkat [3]3 years ago

7 0

Answer:

sorry I need some point

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

Landon is standing in a hole that is 5.1 ft deep. He throws a rock, and it goes up into the air, out of the hole, and then lands

kati45 [8]

This describes a parabolic path that starts at x=0 on a value of y = -5.1. That's when the rock is below ground in the hole. To find the answer we need to know the second x axis crossing. The first is when it is rising and reaches ground level, the second is after it peaks and falls back to the ground and lands. Using the quadratic formula I get the two zeros of this function to be about
x= 15.29, and 66.71. The rock then lands 66.71 feet from him horizontally.

6 0

3 years ago

on a tour of an old gold mine, you find a gold nugget containing .82 ounces of gold. gold is worth $1566.80 per ounce. how much

Andreas93 [3]

1566.80 * 0.82 = 1331.77

6 0

4 years ago

Read 2 more answers

What of b make y = 2x plus b the same as y=2x? What does that value mean?

WITCHER [35]

Answer:

Step-by-step explanation:

The short answer is no. b stands for some number. Once that number is fixed, it does not change. So the equation would look something like

y = 2x + 6 Now if you look at that again, that 6 is fixed.

If you want to put something in for x like x = 5 you get

y = 2(5) + 6

y = 10 + 6

y = 16 b = 6 did not change.

What does y = 2x equal

y = 2*5

y = 10

10 does not equal 16.

The only exception to what I've written is b = 0. Then both equations mean the same thing. But that is an exception.

5 0

3 years ago

Which expression is equivalent to r over s (6)

Goshia [24]

I dont kwon the answer to your question

8 0

4 years ago