Question

trig identities :
tan^2x-sin^2x=tan^2sin^2x

Answer 1

\[\tan^2x-\sin^2x=\tan^2xsin^2x\]
prove the identity.

Answer 2

take left hand side,
rewrite tan as sin/cos

Answer 3

let me show you the work i've done so far.

Answer 4

or a better method would be to leave the `tan ` as it is, and write sin as tan*cos

Answer 5

\[\frac{ 1-sinx }{1+sinx }*\frac{ \cos^2x }{ \cos^2x }= \frac{ \cos^2x(1-sinx )}{\cos^2x(1+sinx }\]

Answer 6

from where u pulled up (1-sinx)/(1+sinx) ?

Answer 7

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

Answer 8

sorry we wrote the wrong problem one sec

Answer 9

starting over lol

Answer 10

take ur time

Answer 11

brain is fried, can u tell?

Answer 12

sin^2x/cos^2x-sin^2x
=(sin^2x-sin^2x.cos^2x)/cos^2x
=sin^2x(1-cos^2x)/cos^2x

Answer 13

do the rest

Answer 14

tan^2xsin^2x= sin^2x=1-cos^2x
tan^2x(1-cos^2x)=tan^2xcos^2x
=tan^2x(-(sinx/cosx)^2cos^2x

Answer 15

whats going on ? :/

Answer 16

sin^2x.sin^2x/cos^2x
=tan^2x.sin^2x

Answer 17

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

Answer 18

oh you're doing it from right hand side is it ?

Answer 19

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

Answer 20

yes

Answer 21

looks great !

Answer 22

now here's my problem

Answer 23

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

Answer 24

what problem ?
you're done lol

Answer 25

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

Answer 26

i'm supposed to prove that the identities equal one another

Answer 27

but i'm at a loss for how to make -(sin^2x/cos^2x)cos^2x into tan^2x

Answer 28

Right hand side :

\(\tan^2x \sin^2x\)

\(= \tan^2x (1-\cos^2x)\)

\(= \tan^2x - \tan^2x \cos^2x\)

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

\(= \tan^2x - \sin^2x\)

= Left hand side.

QED.

Answer 29

got it
idk what iwas thinking

Answer 30

if you're stuck here :

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

Answer 31

they're both are equal

Answer 32

okay, thank you.

Answer 33

simply cancel out \(\cos^2x\) okay ?

Answer 34

yes

Answer 35

agree^ looks ur brain is friend lol put it in freezer somtime :P

Answer 36

*fried