## anonymous 3 years ago Verify that (sin x)(tan x cos x – cot x cos x) = 1 – 2 cos2x

1. anonymous

did you write this down correctly

2. anonymous

yes

3. anonymous

its very confusing

4. anonymous

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

5. anonymous

yes that is what i meant sorry it didnt square it

6. anonymous

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

7. anonymous

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

8. anonymous

ok so cos^2x/sinx ?

9. anonymous

at the end ?

10. anonymous

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. anonymous

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

12. anonymous

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

13. anonymous

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. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

brb though

18. anonymous

ok so ill open another