Question

Verify the identity.

4csc2x = 2csc^2x(tanx)

PLEASE HELP ME IF YOU KINDLY WOULD:)

Answer 1

Express both sides in terms of sine and cosine.
Write cosecant as 1/sine and tangent as sine/cosine:
\(4 \frac{1}{sin(2 x)} = ^?\frac{sin(x)}{cos(x)} 2 ( \frac{1}{sin(x)} ^2 )\)
Simplify the right hand side.
\(2 (\frac{1}{sin(x)})^2 (\frac{sin(x)}{cos(x)}) = \frac{2}{cos(x) sin(x)}:\)
\(\frac{4}{sin(2 x)} = ^?\frac{2}{cos(x) sin(x)}\)
Eliminate the denominators on both sides.
Cross multiply:
\(4 cos(x) sin(x) = ^?2 sin(2 x)\)
Cancel common terms.
Divide both sides by 2:
\(2 cos(x) sin(x) = ^?sin(2 x)\)
Use the double angle identity on \(sin(2 x).\)
\(sin(2 x) = 2 sin(x) cos(x):\)
\(2 cos(x) sin(x) = ^?2 cos(x) sin(x)\)
Come to a conclusion.
The left hand side and right hand side are identical:

Answer 2

Which tells us..?

Answer 3

I'm sorry, I meant to say \(\cos\) and \(\sin\) not \(cos\) and \(sin\)

Answer 4

It's fine.

Answer 5

Tells us that the identity is verified and equal to one another?