Question

Can anyone explain how to prove(sin x)(tan x cos x - cot x cos x) = 1 - 2 cos2x


This proving trig functions has got me confused

Answer 1

write tan in terms of sin over cos
\[\huge\rm tan \theta = \frac{ \sin }{ \cos }\]
change that
and remember cot is reciprocal of tan

Answer 2

\[\large\rm sinx (\color{reD}{tanx} cosx - \color{red}{cotx} cosx)\]\[\large\rm sinx(\color{Red}{\frac{ \sin x}{ cosx }} cosx - \cot x cosx)\]
cot x = what ?

Answer 3

Give me a sec

Answer 4

Sinx(sinx/cosx×cos-cosx/sinx×cosx)
=sin^2x-cos^2x. (Multiply sin inside the bracket)
=-cos2x

Answer 5

The answer is incorrect

Answer 6

\(\color{blue}{\text{Originally Posted by}}\) @lala102
Give me a sec
\(\color{blue}{\text{End of Quote}}\)
okay :-)

Answer 7

Okay i am so confused gahhhh!!! I really hate trig. Do I distribute? I do not know what I am doing, but I'm trying. Math is just my enemy

Answer 8

where is your work ??

Answer 9

cot x = what ?
if tan = sin/cos

Answer 10

Want to solve it then love it play with it .
It's not your enemy.

Answer 11

Oh okay I got you now cotx is 1/tanx right

Answer 12

nope tan and cot are reciprocal of each other
so if tan = sin /cos then cot = cos /sin

Answer 13

\[\large\rm sinx(\color{Red}{\frac{ \sin x}{ cosx }} cosx - \frac{cosx}{sin} cosx)\]
now solve the parentheses first

Answer 14

Um okay.... Man I must be looking at the wrong set of notes. I'm sorry

Answer 15

what do yo mean ??

Answer 16

both sides are equal you can verify

Answer 17

I'm sorry I'm going slow its somethinwrong with my phone

Answer 18

alright
let sin x = a
and cos x = b



\[\large\rm a(\color{Red}{\frac{ a}{ b }}( b)- \frac{b}{a} (b))\]
simple algebra can you solve it now

Answer 19

Yes thank you!

Answer 20

got it ?