## VeroZarate 2 years ago Verify that (sin x)(tan x cos x – cot x cos x) = 1 – 2 cos2x

1. binarymimic

did you write this down correctly

2. VeroZarate

yes

3. VeroZarate

its very confusing

4. binarymimic

are you sure the last one shouldn't be $1 - 2 \cos^{2}(x)$ instead of 1 - 2 cos 2x

5. VeroZarate

yes that is what i meant sorry it didnt square it

6. binarymimic

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

7. binarymimic

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

8. VeroZarate

ok so cos^2x/sinx ?

9. VeroZarate

at the end ?

10. binarymimic

it would become $(\sin x)(\sin x - \frac{ \cos^{2} x }{ \sin x }) = 1 - 2 \cos^{2} x$ then $\sin^{2} x - \cos^{2} x = 1 - 2 \cos^{2} x$

11. binarymimic

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

12. VeroZarate

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

13. binarymimic

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

14. binarymimic

and we have the identity $\sin^{2} x + \cos^{2} x = 1$

15. VeroZarate

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

16. binarymimic

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

17. binarymimic

brb though

18. VeroZarate

ok so ill open another