Question

write the following Trigonometric expression in terms of sinx. csc^2x -cot^2x.

not sure how to go about solving . I got this as my answer but no sure if it is right 1/sin^2x-cos^2x/sin^2x=1

Answer 1

I am so lost

Answer 2

\[\csc^2x -\cot^2x\\=\frac1{\sin^2x}-\frac{\cos^2x}{\sin^2x}\\=\frac{1-\cos^2 x}{\sin^2x}\]

now use \[\sin^2x+\cos^2x=1\qquad\implies 1-\cos^2x=\sin^2x\]

Answer 3

so i was on the right track

Answer 4

yes,

Answer 5

so it all equals to 1
?

Answer 6

thats right \[\huge\color{red}\checkmark\]

Answer 7

they cross cancel eachother out

Answer 8

thank you for your assistance

Answer 9

\[=\frac{1-\cos^2 x}{\sin^2x}\\=\frac{\sin^2x}{\sin^2x}\\=\frac{\cancel{\sin^2x}}{\cancel{\sin^2x}}\\=1\]

good work