Question

Verify that (sin x)(tan x cos x – cot x cos x) = 1 – 2 cos2x

Answer 1

did you write this down correctly

Answer 2

yes

Answer 3

its very confusing

Answer 4

are you sure the last one shouldn't be

\[1 - 2 \cos^{2}(x) \]

instead of

1 - 2 cos 2x

Answer 5

yes that is what i meant sorry it didnt square it

Answer 6

Ok try starting by rewriting tan x as sin x / cos x
and cot x as cos x / sin x

Answer 7

\[(\sin x)(\frac{ \sin x }{ \cos x } * \cos x - \frac{ \cos x }{ \sin x } * \cos x) = 1 - 2 \cos^{2} x\]

Answer 8

ok so cos^2x/sinx ?

Answer 9

at the end ?

Answer 10

it would become

\[(\sin x)(\sin x - \frac{ \cos^{2} x }{ \sin x }) = 1 - 2 \cos^{2} x\]

then

\[\sin^{2} x - \cos^{2} x = 1 - 2 \cos^{2} x\]

Answer 11

last step would just be add 2 cos^2(x) to both sides

Answer 12

i dont understand where the 2cos^2x came from

Answer 13

there is already a -2 cos^2 x in the problem. the last step is to add 2 cos^2 x to both sides

this way the right side becomes: 1
and the left side becomes: sin^2 x + cos^2 x

Answer 14

and we have the identity

\[\sin^{2} x + \cos^{2} x = 1\]

Answer 15

oh ok i understand! thanks! do you think you can help me out with another one?

Answer 16

sure but they recommend you close this question and start another one

Answer 17

brb though

Answer 18

ok so ill open another