Question

how do i factor sin^2x csx^2x - sin^2x

Answer 1

csc*

Answer 2

Take \(sin^2 x\) common from both the terms..

Answer 3

\[\huge = \sin^2x(cosec^2x - 1)\]

Answer 4

Um, isn't
\[sin^2(x)csc^2(x) = \frac{sin^2(x)}{sin^2(x)} = 1\]

Answer 5

And isn't
\[1-sin^2(x) = cos^2(x)\]

Answer 6

He is asking to factorize and not to solve I think..

Answer 7

if i simplified the expression would i get -1? o-o

Answer 8

if you simplify the expression you get
\[cos^2(x)\]

Answer 9

using fundamental identities

Answer 10

really?

Answer 11

after i factor it and simplify

Answer 12

yes
\[sin^2(x)csc^2(x)-sin^2(x) = \frac{sin^2(x)}{sin^2(x)}-sin^2(x) =1-sin^2(x)=cos^2(x)\]

Answer 13

Just need definition of csc and the pythagorean identity:
\[sin^2(x)+cos^2(x)=1\]

Answer 14

but when i factor i get sin^2x (csc^2x-1) ?

Answer 15

That is equivalent, but irrelevant.

Answer 16

csc = 1/sin

Answer 17

sin^2x(cosec^2x-1) .................... since: cosecx=1/sinx

therefore= sin^2x(1/sin^2x-1) multiple sin^2x
therefore=sin^4x(1-sin^2x).............................since:(sin^2x+cos^x)=1
therefore=sin^4x(cos^2x+sin^2x-sin^2x)
therefore=sin^4xcos^2x=sin^2x(sin^2xcos^2x)
since:(2sinxcosx)=sin2x
therefore=sin^2x[0.5sin^2(2x)]

Answer 18

I HOPE IT WORKS !!

Answer 19

sin = O/H cos = A/H tan = O/A
csc = H/O sec = H/A cot = A/O
What you just asked is the same as:
\[(O/H)^2(H/O)^2-(O/H)^2\]

Answer 20

i did i/csc^2x (csc^2x-1) can i cancel out the csc^2x?

Answer 21

\[\frac{O^2}{H^2}\frac{H^2}{O^2}−\frac{O^2}{H^2} =1-\frac{O^2}{H^2}=\frac{H^2}{H^2}-\frac{O^2}{H^2}=\frac{H^2-O^2}{H^2}\]

Answer 22

But Pythagorus taught us:
\[H^2=O^2+A^2\ \ or\ \ H^2-O^2=A^2 \]
\[\frac{H^2-O^2}{H^2}=\frac{A^2}{H^2}= (\frac{A}{H})^2 = cos^2(x)\]

Answer 23

When in doubt, SOHCAHTOA!!!!

Answer 24

haha, i was confused by the variables at first but alright, thanks!

Answer 25

The fact that the trigonometric relationships are defined as these ratios and their relationship in a right triangle is fundamental. Make sure you understand this aspect of trigonometry if you commit anything to memory.