Question

(sin x)(tan x cos x – cot x cos x) = 1 – 2 cos2x

I did this already, but on one part my teacher is confused by it. if u want to help, tell me so i can copy paste my work!!!

Answer 1

@amistre64 @campbell_st @Jaynator495 @Kainui @radar

Answer 2

@KamiBug @JFraser

Answer 3

@ganeshie8

Answer 4

you guys wanna see my work and see if its right? My teacher was only confused at one part

Answer 5

aw man u can't see the exponents cuz i used the exponent button on word, so all the EXPONENTS will be shown as blank BOXES. sorry for that!

Answer 6

tan x cos x sin x – cot x cos x sin x

sin⁡x/cos⁡x cos x sin x - cos⁡x/sin⁡x cos x sin x

sin⁡x/cos⁡x cos x sin x - cos⁡x/sin⁡x cos x sin x

Sin2 x – cos2 x

Use the Identity- Cos(2x)= cos2 x – sin2 x = 2 cos2 x -1 <-part that confused her
Sin2 x – cos2 x

= -1(cos2 x – sin2 x)
= -1(2 cos2 x -1)
= -2 cos2 x +1
= 1-2 cos 2 x

Answer 7

wait Ima do a screenshot! would that be better?

Answer 8

well look at the left hand side and make some simple substitutions

tan = sin/cos and cot = cos/sin

so you get

\[\sin(x)(~~\frac{\sin(x)}{\cos(x)} \times \cos(x) - \frac{\cos(x)}{\sin(x)} \times \cos(x))\]

simplify the part inside the brackets and post your solution

Answer 9

so do i eliminate all the cos(x) and sin(x) that match up

Answer 10

your working makes sense

Answer 11

but what about the "identity " part?

Answer 12

look at the screenshot u can see it way better there

Answer 13

well I would to the bracket simplification 1st before multiplying by sin(x) it just reduces clutter

Answer 14

ur talking about my work above right^^^

Answer 15

can u write it out for me plzz

Answer 16

idk how to simplify inside the brackets with sin x and cos x

Answer 17

so I would have

\[\sin(x) ( \sin(x) - \frac{\cos^2(x)}{\sin(x)})\]

now multiply and get

\[\sin^2(x) - \cos^2(x)\]

then I would use a substitution

\[\sin^2(x) + \cos^2(x) = 1~~~~so~~~~~\sin^2(x) = 1 - \cos^2(x)\]

which means you get

\[(1 - \cos^2(x) - \cos^2(x)) = 1 - 2\cos^2(x)\]

your method is find, just a bit long winded... and can be reduced by just using the basic identity and rewriting it...

hope it makes sense.

Answer 18

thanks so much!! can u help me correct 2 more plz? the next one is super short

Answer 19

@campbell_st

Answer 20

#4 she said first step isnt clear

Answer 21

for #5 she said yes, so....go ahead and make the substitution

Answer 22

but for #5 idk what to do

Answer 23

ok... so for 4... again you need sin^2 + cos^2 = 1

cross multiply and get a common denominator and you have

\[\frac{\sin(x)(1 + \cos(x) 1 - \cos(x))}{1 - \cos^2(x)}\]

make the substitution in the denominator

\[\frac{\sin(x)( 1 + \cos(x) 1 - \cos(x))}{\sin^2(x)}\]

cancel the common denominator and simplify the numerator and its

\[\frac{2}{\sin(x)} = 2 \times \frac{1}{\sin(x)} = 2 \csc(x)\]

Answer 24

#5!!!! @campbell_st

Answer 25

its above^

Answer 26

#5, well use the identity and replace sec^2 with 1 + tan^2

then collect like terms and see what happens.... look at the sign of the 1st term

Answer 27

-1 ?

Answer 28

or 1?

Answer 29

it should equal 1 right, otherwise the identity wouldnt even make sense

Answer 30

does this look okay



Identity: sec^2 x = 1 + tan^2 x
= -tan^2x + 1 + tan^2
=1

Answer 31

that's correct

Answer 32

k thanks so muuuch

Answer 33

@JFraser u came after we r already done...