Question

Prove that 1-2cos^2x=sinxcosx(tanx-cotx)

Answer 1

\[1-Cos^2x=SinxCosx(Tanx-Cotx)\]
lets translate everything in terms of sines and cosines.
\[1-2Cos^2x=SinxCosx(\frac{Sinx}{Cosx}-\frac{Cosx}{Sinx})\]now, lets simplify the left side.\[SinxCosx\frac{Sinx}{Cosx}-SinxCosx\frac{Cosx}{Sinx}--->Sin^2x-Cos^2x\]so we have\[1-2Cos^2x=Sin^2x-Cos^2x\]add Cos^2x to both sides
\[1-2Cos^2x+Cos^2x=Sin^2x-Cos^2x+Cos^2x-->1-Cos^2x=Sin^2x\] add Cos^2x to both sides,\[1=Sin^2x+Cos^2x\]
Bingo!!!!!!!!!!

Answer 2

I understand when you made Tangent into Sine/Cos and Cotagent being the reciprocal but then you lost me after that....soory?

Answer 3

@SolomonZelman After you are done here.. Can you help me on a math problem?