Question

MEDALS!!! Simplify the expression: 1/1+cot^2x
a.sec^2x
b.csc^2x
c.sin^2x
d.cos^2x
e.tan^2x

Answer 1

rewrite cot^2x in terms of sin cos
cotx= ??

Answer 2

there i fixed it

Answer 3

yep okay thanks. so how would you write cotx in terms sin cos ?

Answer 4

idk

Answer 5

here is good website where you can find all trig ratios,identities, formulas
scroll down where it says `Relations Between Trigonometric Functions`

sin is reciprocal of 1/csc
\[\sin x= \frac{1}{cscx}~~~~~~~~\cos x= \frac{1}{secx}~~~~~~~~\tan =\frac{1}{cotx}=\frac{\sin x}{cosx}\]

Answer 6

if tanx = sinx/cosx
then cot x= cosx/sinx

Answer 7

that's how you should rewrite ratios in terms of sin ,cos
so rewrite cot^2x as cos^2x over sin^2x

Answer 8

\[\large\rm \frac{ 1 }{ \color{ReD}{1+\frac{ \cos^2x }{ \sin^2x } }}\]
simplify the red part first (find the common denominator )

Answer 9

so is it c

Answer 10

what's the common denominator ??

Answer 11

idk

Answer 12

so then how did you get C ??

Answer 13

i saw sin^2x as the denominator

Answer 14

\[ \large\rm 1+\frac{ a }{ b }\]
which is same as \[ \large\rm \frac{1}{1}+\frac{ a }{ b }\]
to find the common denominator
the first fraction by b/b \[\frac{ b }{ b } \cdot \frac{ 1 }{ 1 } +\frac{ a }{ b }=\frac{ b }{ b }+\frac{a}{b}\] now i have the same denominator i can rewrite it as single fraction \[\frac{ b+a }{ b }\]

Answer 15

do the same thing with \[1+\frac{\cos^2x}{\sin^2x}\]

Answer 16

sin^2x + cos^2x
sin^2x

Answer 17

so d

Answer 18

do you mean over sin^2x ??
\[\frac{ 1 }{ \frac{ \sin^2x+\cos^2x }{ \sin^2x } }\]

Answer 19

yes

Answer 20

so what is the famous identity ??
sin^2x +cos^2x = ??

Answer 21

idk how you type it

Answer 22

thats fine but you can use VVVequation tool :)

Answer 23

\[\large\rm \frac{ 1 }{ \frac{ \color{Red}{\sin^2x+\cos^2x} }{ \sin^2x } }\]what is that red part equal to ?

Answer 24

1?

Answer 25

right \[\large\rm \frac{ 1 }{ \frac{ \color{Red}{1} }{ \sin^2x } }\]
\[\large\rm \frac{ 1 }{ \frac{ a }{ b } } =1 \cdot \frac{ b }{ a }\]
multiply the top with the reciprocal of the bottom fraction that's it !

Answer 26

so sin^2 x

Answer 27

yep

Answer 28

ok thanks

Answer 29

np