Question

x

Answer 1

(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos^2 x

Answer 2

anx = (sinx/cosx)
cotx = (cosx/sinx)

sinx cosx (tanx - cot x) = sinx cosx (sinx/cosx - cosx/sinx)
Cross multiply the equation in the braket and make the in same denomenator.
=sin x cos x ((sin^2x - cos^2x)/(cosx sinx))
= sin^2x - cos^2x
Replace sin^2 by 1 - cos^2x
= 1 - cos^2x - cos^2x
= 1 - 2cos^2x

Answer 3

http://ca.answers.yahoo.com/question/index?qid=20091119205416AAdnUV9

Answer 4

\[\begin{align*}\sin x\left(\tan x\cos x-\cot x\cos x\right)&=1-2\cos^2x\\
\sin x\left(\frac{\sin x}{\cos x}\cos x-\frac{\cos x}{\sin x}\cos x\right)&=\\
\sin x\left(\sin x-\frac{\cos^2 x}{\sin x}\right)&=\\
\sin^2 x-\cos^2 x&=\\
-\left(\cos^2x-\sin^2 x\right)&=\\
-\cos(2x)&=\\
-\left(2\cos^2x-1\right)&=\\
\end{align*}\]