Question

prove the following identities
csc(theta) - sin (theta) = cos(theta*cot(theta)

Answer 1

probably nothing but a bunch of algebra. easier to do if you replace cosine by "a" and sine by "b" and compute
\[\frac{1}{b}-b=a\times \frac{a}{b}\]

Answer 2

on the left hand side you get
\[\frac{1-b^2}{b}\] on the right hand side you get
\[\frac{a^2}{b}\] so you want so show that
\[\frac{1-b^2}{b}=\frac{a^2}{b}\] now go back to trig and get
\[\frac{1-\sin^2(x)}{\sin(x)}=\frac{\cos^2(x)}{\sin(x)}\] and since
\[1-\sin^2(x)=\cos^2(x)\] you get what you want

Answer 3

thank you, can i ask one more question?