Question

1+cos(2x) = cot(x)sin(2x)

Answer 1

1+cos 2x = 2cos^2 x
so u have to now prove cot x sin2x = 2cos^2 x
write cot x as cos x/sin x
and sin 2x as 2 sin x cos x
got this? can u go further?

Answer 2

Thank you for your response. This is as far as I was able to make it. I was able to simplify the LS to 2(1-sin^2x), although i'm not sure if this is correct.

It's the RS that confuses me the most (below is the best i can do)
\[\frac{ \cos(x) }{ \sin(x)} * 2\sin(x)\cos(x) \]Any further help would be appreciated (I'm helping Gohan with his math homework, wouldn't want to make him angry :P )

Answer 3

your LS=2(1-sin^2 x)=2cos^2 x because sin^2x + cos^2 x = 1
in RS , u can cancel out sin x from numerator and denominator,which directly gives u 2 cos^2 x
so LS=RS=2cos^2 x !!
Hence,1+cos(2x) = cot(x)sin(2x)

Answer 4

Wow, thank you! I did not know that you could cancel out the sin(x). Thank you for teaching me that, it will definitely help me in the future.

Answer 5

welcome :)