Question

Write the trigonometric expression in terms of sine and cosine, and then simplify.
csc2 x − cot2 x

Answer 1

whats csc x in terms of sin x ?

Answer 2

thats what i do not know

Answer 3

csc x = 1/sin x

Answer 4

and cot x in terms of sin and cos is ?

Answer 5

cos/sin

Answer 6

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

Answer 7

that is correct, now just put both the formulas in the question,
csc x = 1/ sin x and cot x = cos x / sin x

Answer 8

or u can see @Zekarias solution and ask if u don't understand any of thhe step...

Answer 9

so 1-cos^2x = sin ^2 x ?

Answer 10

yep

Answer 11

thats from the identity \(\huge sin^2x+cos^2x = 1\)

Answer 12

ohh that makes sense. i remember now thanks