Question

can someone help me simplify this equation using identities. The equation is sin(x)/√1-sin²

Answer 1

mathmale

Answer 2

do you know an identity that uses 1 - sin^2 ?

Answer 3

yeah there trigonometric identities

Answer 4

and which one has 1 - sin^2 ?

Answer 5

the very bottom one but what do I do I am very confused

Answer 6

would we have to convert sin into tan or cos

Answer 7

if it helps, a very famous identity is
\[ \sin^2 x + \cos^2 x = 1\]
from this you can get two useful identifies

Answer 8

for example, if you subtract cos^2 x from both sides you get
\[ \sin^2 x + \cos^2 x = 1 \\
\sin^2 x + \cos^2 x - \cos^2 x = 1 - \cos^2 x\]
the left side simplifies, so you get
\[ \sin^2 x = 1 - \cos^2 x\]

Answer 9

then what do I do

Answer 10

you can also subtract sin^2 x from both sides to get
\[ \cos^2 x = 1 - \sin^2 x\]
I would use that identity

Answer 11

would we then put it into the equation and solve it so we change it to cos but how do we get rid of the square root and such

Answer 12

the definition of
\[ \sqrt{x\cdot x} = x \]
no matter how complicated x is
as you know \(\cos^2 x \) is short for \( \cos x \cdot \cos x \)

Answer 13

in other words you have cos x times itself inside a square root
\[ \sqrt{ \cos(x) \cdot \cos(x) } \]

Answer 14

could we get rid of the square root and the squared symbol since they both will get rid of each other so what we are stuck with are 1-sin

Answer 15

just looking at the bottom:
\[ 1 - \sin^2 x \]
by the identity you know that is the same as
\[ \cos^2 x \]
the 1- sin^2 x is *replaced* by cos^2 x

Answer 16

so you have
\[ \frac{\sin x}{\sqrt{\cos x \cdot \cos x } } \]

Answer 17

and you know how to simplify sqr( a*a) to get a, right ?

Answer 18

remember sqrt( anything * anything) = anything

Answer 19

I get it now thanks for the help because sinx/cosx. Thanks for the help how do I medal I am new to openstudy

Answer 20

notice that tan x = sin(x)/cos(x)
they may want you to answer with tan x

Answer 21

sorry forgot to say that thanks anyway now how do I medal

Answer 22

you click "best response" , like this

Answer 23

thanks for the help

Answer 24

yw