Question

Verify the identity. 1 + sec^2xsin^2x = sec^2x can someone help me

Answer 1

simplify sec^2x into something using cosine
recall that sin/cos = tan
and that cos/sin = cot

Answer 2

@dan815

Answer 3

hey super

Answer 4

i could use the help

Answer 5

do you know trig identities ??
sec = ??
sin = ??
cos = ??

Answer 6

no not exactly

Answer 7

learn your damn identities
you don't want help

Answer 8

i need someone to walk me through this listen the truth is im taking the class but im running out of time and need months to learn pre calc but only have a week before i cant do school work anymore sorry but i need this done so im open to patially doin this but i need someone to help me with it too

Answer 9

hmm should be on ur notes
well
\[\large \rm sec = \frac{ 1 }{ \cos }\]
\[\csc = \frac{ 1 }{ \sin }\]
\[\cot = \frac{ 1 }{ \tan}\]
reciprocal functions:
\[\cos = \frac{ 1 }{ \sec}~~~~\] \[\sin = \frac{ 1 }{ \csc}\]
\[\tan = \frac{ \sin }{ \cos }\]
memorize it write these "n ur notebook

Answer 10

so you have to prove that
RHS = RHS
\[\huge\rm 1+\sec^2x~sin^2x\]
change sec^2 by its reciprocal

Answer 11

@Nnesha ok i copied those functions in my notes

Answer 12

good :)

Answer 13

okay look at the identities find sec^2 = what ??

Answer 14

sec^2=1^2/cos^2?

Answer 15

yes right
1^2 =1 so we can write \[\sec^2 = \frac{ 1 }{ \cos^2}\]

Answer 16

so would sec^2(x)-1/cos^2(x)

Answer 17

\[\huge\rm 1+\sec^2x~sin^2x\]
replace sec^2 by 1/cos^2

Answer 18

\(\color{blue}{\text{Originally Posted by}}\) @quick24
so would sec^2(x)-1/cos^2(x)
\(\color{blue}{\text{End of Quote}}\)
if you meant "equal" sign then yes

Answer 19

yes thats what i meant so my equation becomes
1+cos^2(x)sin^2(x)=1/cos^2(x)

Answer 20

well not really
bec we are solving LHS to prove that is equal to RHS

Answer 21

so we leave the right hand side the same

Answer 22

like at the right side there is only one term which is sec^2
yes right stays same bec we havve to prove that LHS = RHS (which is sec^2x)

Answer 23

ok

Answer 24

so my left hand side should like like this
1+cos^2(x) 1/csc^2(x)

Answer 25

sorry 1+1/cos^2(x) 1/csc^2(x)

Answer 26

nope