Question

Prove the following identity:
(sin x)(tan x cos x - cot x cos x)=1-2cos^2 x

Answer 1

\[tanx = \frac{ sinx }{ cosx }\]
\[cotx = \frac{ cosx }{ sinx }\]

Knowing this than you can substitute to get the following.

\[(sinx)\frac{ sinx }{ cosx }(cosx) - \frac{ cosx }{ sinx }(cosx)\]

now you can simplify to get..\[\sin ^{2}x - \frac{ \cos ^{2} x}{ sinx }\]

can you take it from there knowing that \[\sin ^{2}x + \cos ^{2}x = 1 \]

Answer 2

thank you