verify the identity of sin2x-tanx=tanxcos2x

[sct11]

i am having trouble verifying the identity of sin2x-tanx=tanxcos2x
any help would be greatly appreciated!

 

[Aladdin]

ok, Please show us some work to help you .

2sinx.cosx-sinx/cosx

Obviously: Same denomenator:

[(cosx)(2sinx.cosx)-sinx]/cosx

[2sinx.cos^2(x) - sinx]/cosx

(sinx)(2cos^2(x)-1]/cosx

(sinx)/cosx.cos(2x)

tanx.cos(2x)

 

[Deleted member 4993]

i am having trouble verifying the identity of sin2x-tanx=tanxcos2x
any help would be greatly appreciated!

Attack the right-hand-side

tan(x) * cos(2x)

= tan(x) * (2cos[sup:1hd4bcl1]2[/sup:1hd4bcl1](x) -1)

= 2tan(x) * cos[sup:1hd4bcl1]2[/sup:1hd4bcl1](x) - tan(x)

= 2sin(x)/cos(x) * cos[sup:1hd4bcl1]2[/sup:1hd4bcl1](x) - tan(x)

= 2sin(x) * cos(x) - tan(x) .... and continue...

 

[Aladdin]

i am having trouble verifying the identity of sin2x-tanx=tanxcos2x
any help would be greatly appreciated!

Attack the right-hand-side

You can use either sides to prove.

 

[mmm4444bot]

You can use either [side] to prove.

Yup, yup.

When proving identities, you can also change both sides to match, if you like.

 

[Aladdin]

Re:

You can use either [side] to prove.

Yup, yup.

When proving identities, you can also change both sides to match, if you like.

Yes, I see.