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

Question

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

hartnn · Answer

whats csc x in terms of sin x ?

anonymous · Answer

thats what i do not know

hartnn · Answer

csc x = 1/sin x

hartnn · Answer

and cot x in terms of sin and cos is ?

anonymous · Answer

cos/sin

anonymous · Answer

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

hartnn · Answer

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

hartnn · Answer

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

anonymous · Answer

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

anonymous · Answer

yep

hartnn · Answer

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

anonymous · Answer

ohh that makes sense. i remember now thanks