Verify the following equation:

\[
\frac{2\cos2x}{\sin2x} - \cot x - \tan x = -2\tan x
\]

Remember:
s in ( 2 x ) = 2. s in x . cos x ​ an d cos ( 2 x ) = co s 2 x − s i n 2 x ​
s in 2 x 2 cos 2 x ​ − co t x − t an x = 2 s in x . cos x 2 ( co s 2 x − s i n 2 x ) ​ − s in x cos x ​ − cos x s in x ​ = s in x . cos x co s 2 x − s i n 2 x ​ − s in x cos x ​ − cos x s in x ​ = s in x . cos x co s 2 x − s i n 2 x − co s 2 x − s i n 2 x ​ = s in x . cos x − 2 s i n 2 x ​ = cos x − 2 s in x ​ = − 2. t an x

Answered by Ryan2 | 2024-06-10

The equation s i n 2 x 2 c o s 2 x ​ − cot x − tan x = − 2 tan x has been verified by simplifying the left-hand side and showing it equals the right-hand side. This verification involves applying trigonometric identities and algebraic manipulation. Ultimately, both sides of the equation are equal to − 2 tan x .
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Answered by Ryan2 | 2025-05-08