1 - tanx sinx = cos2x + sin²x

I think i finally created a proper iidentity.. I just need somebody to try and prove it!

Thanks

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- Apr 18th 2010, 09:20 PMadvancedfunctions2010Please Bare with Me.. Can you prove this identity?
1 - tanx sinx = cos2x + sin²x

I think i finally created a proper iidentity.. I just need somebody to try and prove it!

Thanks - Apr 18th 2010, 09:30 PMMacstersUndead
- Apr 18th 2010, 09:36 PMadvancedfunctions2010
Im not sure what you mean?

- Apr 18th 2010, 09:41 PMharish21
$\displaystyle LHS = 1 - (tanx \times sinx) $

$\displaystyle = 1 - \frac{sinx}{cosx} \times sinx $

$\displaystyle = 1-\frac{sin^2x}{cosx}$

$\displaystyle RHS = cos2x + sin^2x = cos^2x-sin^2x+sin^2x =cos^2x $

So the identity you have created cannot be equal.

however, if you change your LHS to :

$\displaystyle 1 - (tanx \times sinx \times cosx) $

$\displaystyle = 1 - (\frac{sinx}{cosx} \times sinx \times cosx) $

$\displaystyle = 1-(sinx \times sinx) = 1-(sin^2x) = cos^2x$

In this case, your RHS will be equal to LHS giving you a proper identity.