Question

verify each identity

Answer 1

Whats the question

Answer 2

k

Answer 3

do you know what mean csc x ?

Answer 4

so csc x = ?

and how can you rewriting cot x and tan x using sin x and cos x ?

Answer 5

@mathstudent55

Answer 6

ITS NUMBER 2 IN THE PICTURE

Answer 7

\(\sin (x + \pi) = -\sin x\)

Answer 8

yes i got that part do you want to see my work?

Answer 9

No, I don't see your work. i only see the question in the figure.

Answer 10

Ok, let's take it from the beginning.

\(\Large \dfrac{\sin (x + \pi)}{\cos (x + \frac{3\pi}{2})} = \tan^2 x - \sec^2 x\)

Answer 11

that's my work

Answer 12

We use the identity for sin & cos of sums:

\(\Large \dfrac{\sin x \cos \pi + \sin \pi \cos x}{\cos x \cos \frac{3\pi}{2} - \sin x \sin \frac{3\pi}{2}} = \tan^2 x - \sec^2 x\)

Answer 13

I see your work now.
So far we have exactly the same.

Answer 14

Now let's take the sin & cos of pi and 3pi/2

Answer 15

did i get that part right?

Answer 16

\(\Large \dfrac{(\sin x )(-1) + (0) \cos x}{(\cos x)(0) - (\sin x)(-1)} = \tan^2 x - \sec^2 x\)

Answer 17

You are very close, but I think you have a 1 where it should be -1 as the sin 3pi/2 at the end of the denominator.

Answer 18

what is sin of 3pi/2?

Answer 19

is it 1?

Answer 20

\(\Large \dfrac{-\sin x }{\sin x} = \tan^2 x - \sec^2 x\)

Answer 21

sin 3pi/2 = -1

Answer 22

HOW DID YOU FIND THE OUT?

Answer 23

since it's -1 wouldnt be postive because it's 0-sin(-1) = 0+sin(1)