Question

How do I simplify sinx(1/cosx) ?

Answer 1

lol sin x/cos x = tan x
:D

Answer 2

how did you get that? :o

Answer 3

sin x = altitude/hypotenuse
cos x = base/hypotenuse
sinx/cosx = (altitude/hypotenuse)/(base/hypotenuse)
= altitude/base (hypotenuse cancel each other)
which is out own tan x :P

Answer 4

our*

Answer 5

so will (cosx)(tanx) be (cosx/tanx)(sinx/cosx) ?

Answer 6

cos x tan x = cos x (sin x /cos x) = sin x

Answer 7

oh okay thanks

Answer 8

what about 1-cos^2x ? will it be sin^2x?

Answer 9

Yes

Answer 10

and 1-sin^2x will be cos^2x? wow thank you :)

Answer 11

sin^2x+cos^2x = 1
sec^2x = 1 + tan^2x
cosec^2x = 1 + cot^2x
(Most important formulae) :P

Answer 12

oh okay yes. um what wiill cos^2x+sin^2x be? would I do this, 1-sin^2x+1-cos^2x ? which would be -sin^2x-cos^2x ?

Answer 13

first of all.. x + y = y + x

-sin^2x-cos^2x = -(sin^2x+cos^2x) = -1

Answer 14

sin^2x+cos^2x = 1 = cos^2x+sin^2x

Answer 15

ohh yes. omg thank you sooo much ! I am very grateful :)

Answer 16

Happy to help :))

Answer 17

(1-sinx)(1+sinx) would be 1^2-sinx^2 ?

Answer 18

do I expand or replace the sinx with tanx/cosx?

Answer 19

why would you replace.. first one is correct

Answer 20

which is also cos^2x

Answer 21

thanks !

Answer 22

for tanx/sinx would I do sinx/cosx times tanx/cosx?

Answer 23

then sinxtanx/cosx^2 ? :S

Answer 24

why are you making it so complicated.. be cool :P

Answer 25

then what should I do? :(

Answer 26

remember tan x = sinx/cosx
cot x = cosx/sinx

Answer 27

so if it is tanx/sinx dont I put sinx/cox for tanx ? replace it? and for sinx I would puttanx/cosx? :S Im confused

Answer 28

yes u can do that.. remember that if it is an identity u can replace everything to simplify

Answer 29

in tanx/sinx .. if u put tanx=sinx/cosx... sinx will cancel each other and u get 1/cosx

Answer 30

which is also sec x =)

Answer 31

hmm okayy. well for 1+tan^2x/tan^2x, will I replace the tan^2x with sec^2x ?

Answer 32

noooo.. replace 1+tan^2x with sec^2x NOT the tan^2x alone

Answer 33

OH okay, then what ?

Answer 34

what "then what"

Answer 35

@apoorvk

Answer 36

well after i sub in, 1+sec^2x-1/tan^2x what do I do ? the 1 cancels out right? then i have sec^2x/tan^2x

Answer 37

yup

Answer 38

okay thannn what should I do? becaue im suppose to get 1/sin^2x :(

Answer 39

sec^2x/tan^2x = cos^2x/sin^2x.cos^2x
cos^2x cancel.. and 1/sin^2x remains

Answer 40

achaaa, okay thank you soooo much !

Answer 41

for sinxcosx/1-sin^2x, i would do sinxcox/1, then would I replace sinx or cosx?

Answer 42

the answer is sinx cosx .. nothing to simplify here

Answer 43

but in my book it says the answer is tanx

Answer 44

oops.. lol.. my mistake

its sinxcosx/cos^2x
= sinx/cosx = "the answer"

Answer 45

what happenes to the cos^2x?

Answer 46

X/X^2 = ??

Answer 47

x ?

Answer 48

oh nvm I get it ! :D

Answer 49

so 1-cos^2x it says factor. it says (1+cosx)(1-cosx) but why can't it be sin^2x?

Answer 50

it can be..

Answer 51

oh okay

Answer 52

convert in a way so that it can be simplified..

Answer 53

alright, thanks man !

Answer 54

it comes with practice.. (solved examples also)

Answer 55

aha yeah it does. I need alot since I just started