Question

Verify the identity.

4 csc 2(x) = 2 csc^2(x) tan x
I work on this for 10 min and couldnt figure out what i did wrong! Help please! :)

Answer 1

*4csc(2x)* instead of 4csc 2(x)

Answer 2

\[4\csc2x=\frac{4}{\sin2x}=\frac{4}{2\sin x\cos x}=\frac{2}{\sin x\cos x}\]
Try working with that now.

Answer 3

Thank you! It makes sense now! :D

Answer 4

\[4 cosec2(x) = 2 cosec^2(x) \tan x \]
LHS=4 cosec2(x)
\[=\frac{4}{\sin2x}\]
\[=\frac{4}{2sinx cosx}=\frac{2}{sinx cosx}\]
Multiplying Nr. and Dr. by sinx we find
\[\frac{2sinx}{\sin^2x cosx}=2 \frac{1}{\sin^2x }\frac{sinx}{cosx} = 2cosec^2 x \tan x\]
=RHS
Thus proved