Question

Graph the expression sec2 x - sec2 x sin2 x on your calculator. Determine what constant or single function is equivalent to the given expression.

Answer 1

-tan(x-45) in deg mode

Answer 2

I don't usually just give answers like that, but I just got it by trial and error.

Answer 3

so tan^-1 (45degrees)

Answer 4

No, not inverse tan, negative tan

Answer 5

oh okay and if I put that down it'll be the right answer?

Answer 6

It is the exact same graph on my calculator.

Answer 7

oh okay awesome! thank you so so so so so so so so so so so much!!!!!

Answer 8

Glad to help :)

Answer 9

I have one more more quick question on another problem

Answer 10

Ok

Answer 11

sin (x + y) - sin (x - y) = 2 cos x sin y
Is this saying that on the right side there are 2cos(x)'s and 2 sin(y)'s

Answer 12

that's wrong

Answer 13

$$\sec^2(x)-\sec^2(x)\sin^2(x)=\sec^2(x)(1-\sin^2(x))=\sec^2(x)\cos^2(x)=1$$given \(\sec(x)=\dfrac1{\cos x}\)

Answer 14

so it's identical to the graph of \(y=1\)

Answer 15

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

the \(2\cos(x)\sin(y)\) means \(2\cdot\cos(x)\cdot\sin(y)\) i.e. multiply them all together

Answer 16

I did sec(2x)-sec(2x)sin(2x)

Answer 17

why of y=1? wouldn't it be of sec(x) because that's what 1/cosx is the identity of?

Answer 18

@help!!!!! \(\sec^2(x)\cos^2(x)=\dfrac1{\cos^2(x)}\cdot\cos^2(x)=1\)

Answer 19

that would be correct, then, @JoannaBlackwelder, but the question explicitly states

>Determine what constant or single function is equivalent to the given expression.

suggesting it's actually \(\sec^2(x)-\sec^2(x)\cos^2(x)\). @help!!!!! should tell us which it is

Answer 20

I can't because I have an online graphing calculator for this class that won't graph this expression

Answer 21

We want to know what the problem statement says.

Answer 22

Is it a double angle or a squared function?

Answer 23

Graph the expression sec2 x - sec2 x sin2 x on your calculator. Determine what constant or single function is equivalent to the given expression.
These are the directions I was given, word-for-word

Answer 24

each of the twos are squares

Answer 25

so which answer is correct?

Answer 26

Oh, ok. Then mine is wrong.

Answer 27

so the other one is correct?

Answer 28

Right.

Answer 29

how about the other problem
Verify the identity.
sin (x + y) - sin (x - y) = 2 cos x sin y

Answer 30

Looks like you will need to use sum and difference formulas.

Answer 31

thats what I was thinking of but I'm sure quite how to use them

Answer 32

@help!!!!! replace \(\sin(x+y)=\sin x\cos y+\cos x\sin y\) and \(\sin(x-y)=\sin x\cos y-\cos x\sin y\)

Answer 33

$$\begin{align*}\sin(x+y)-\sin(x-y)&=(\sin x\cos y+\cos x\sin y)-(\sin x\cos y-\cos x\sin y)\\&=\sin x\cos y+\cos x\sin y-\sin x\cos y+\cos x\sin y\end{align*}$$

Answer 34

try to simplify that... also my previous answer was correct...

Answer 35

does it simplify to 2sinxcosy2sinycosx?

Answer 36

and okay

Answer 37

not quite... notice it's \(\sin x\cos y+\dots\color{red}-\sin x\cos y+\dots\)

Answer 38

so the \(\sin x\cos y\) terms cancel out giving us just \(\cos x\sin y+\cos x\sin y\) -- can you combine like terms? hint: \(a + a = 2a\)

Answer 39

ohhhhhhhhhhh okay I see now, so then after they cancel out I'm left with 2cosx siny

Answer 40

exactly! :-)

Answer 41

awesome you are the greatest thank you for clearing the confusion with the coefficients :-) goodnight!