Question

Prove the following identities:
1.) (tan^2 x) (sin^2 x) + sin^2 x = tan^2 x
2.) sin^2 x + cos^2 x = csc^2 x + sin^2 x
3.) (sin x + cos x) sin x = 1 - cos x (cos x - sin x)
HELP ME PLEASE.. :D

Answer 1

factor out sin^2x from the first equation's left side, what you get ?

Answer 2

how to factor po?

Answer 3

(tan^2 x) (sin^2 x) + sin^2 x
=[(tan^2 x)+1] (sin^2 x)
=[.......] sin^2 x
can you fill the blank using a pythagorean identity ?

Answer 4

hm, yes po. the answer is sec^2 x ?

Answer 5

yes,
so sec^2x * sin^2 x =... ?

Answer 6

hm, i don't know the answer. hm, is sec^2x * sin^2 x has a formula?

Answer 7

no, but sec^2x = 1/cos^2 x
and sin^2x /cos^2x = tan^2 x
which proves the first identity, got it ?

Answer 8

no .. i didn't get. im so sorry. im so slow. ahm , how did you get [(tan^2 x)+1] (sin^2 x)

Answer 9

by factoring out sin^2x
its similar to (s+st) = s(1+t)

Answer 10

ahh. :D now i know, i get it .. but how abou this : sec^2x * sin^2 x ?

Answer 11

sec = 1/cos
so, sec^2x * sin^2 = sin^2 / cos^2

and tan=sin / cos
so, sin^2 / cos^2 = tan^2 = right side.

Answer 12

ahh.. i get it .. :D thank you po . :D hm, how about #2? will you help me on that?

Answer 13

#2 isn't an identity, it can't be proved.
unless you have typed the question incorrectly...

Answer 14

i can help you with #3 , if you still need it.

Answer 15

ahh .. that's why i can't prove it .. thank you po . hm, yes .. #3 pls.

Answer 16

do you know, sin^2 +cos^2 =.... ?

Answer 17

yes .. it is equal to 1.

Answer 18

good, so from that sin^2+cos^2=1
what will sin^2 x =... ?

Answer 19

ahm , 1 - cos^2x ? am i right?

Answer 20

correct :)

Answer 21

(sin x + cos x) sin x
= sin^2x + sin x cos x
now put here, the value of sin^2x you got,

Answer 22

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

Answer 23

good! so you got 3rd by yourself :)
nice work...

Answer 24

ahh .. is that all only ?

Answer 25

es, we proved left side = (sin x + cos x) sin x
= sin^2x + sin x cos x
=1 - cos^2x + sin x cos x
= 1 - cos x (cos x - sin x)
=right side
so its an identity.....

Answer 26

and bdw, i see this is your first day here, so
\(\huge \color{red}{\text{Welcome to Open Study}}\ddot\smile\)

Answer 27

ahh.. thank you so much po. :D hm, it's not my first day here po , i just make a new account po because i can't use the other one . :D but, thank you po for noticed me .. :D

Answer 28

can i ask you a question ?
whats a 'po' ?

Answer 29

ahm sure po . hehe .. i'm a FILIPINO po then we used "po" po in respecting someone ..

Answer 30

ohhh..thanks :)
can i ask you one more question ?
is you real name Quennie ?
if you don't want to, don't answer...

Answer 31

aaah...i see you have updated your profile, and it is :)

Answer 32

hm, always welcome po. hehe, yes. that's my real name .. im QUENNIE DIMAANO po. haha! :D thank you again po.

Answer 33

just so that you know, that i am also a math lover :)

Answer 34

ahh .. yes . . i already know that po .. :D