Hey, I have a few questions I just can't seem to get down, looking for some help here...

1)sin2x= 2csc2x-tanx

1-cos2x

2) cos(x+y)cos(x-y)=(cosx)^2 +(cosy)^2 -1

3) (cosx)^6 + (sinx)^6 = 1-3(sinx)^2 + 3(sinx)^4

Thanks in advance! :D

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- May 27th 2010, 01:06 PMorca432Proving Trig Formulas
Hey, I have a few questions I just can't seem to get down, looking for some help here...

1)__sin2x__= 2csc2x-tanx

1-cos2x

2) cos(x+y)cos(x-y)=(cosx)^2 +(cosy)^2 -1

3) (cosx)^6 + (sinx)^6 = 1-3(sinx)^2 + 3(sinx)^4

Thanks in advance! :D - May 27th 2010, 01:35 PMharish21
You need to show you work too..

(2) $\displaystyle cos(x+y)cos(x-y) = (cosx.cosy-sinx.siny)(cosx.cosy+sinx.siny)$

$\displaystyle = (cos^2x.cos^2y) - (sin^2x.sin^2y)$

$\displaystyle = (cos^2x.cos^2y) - [(1-cos^2x)(1-cos^2y)]$

multiply and cancel to complete the proof - May 27th 2010, 01:46 PMharish21
for (3)

$\displaystyle (cosx)^6+(sinx)^6$

$\displaystyle = (cos^{2}x)^3 + (sin^{2}x)^3$

since $\displaystyle (a^3+b^3) = (a+b)(a^2-ab+b^2)$, you can write:

$\displaystyle = (cos^{2}x+sin^{2}x)(cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$

$\displaystyle = 1 (cos^{4}x-cos^{2}x. sin^{2}x+sin^{4}x)$

convert all cosines into sines and your proof will be complete. - May 27th 2010, 03:13 PMorca432
- May 27th 2010, 03:54 PMharish21
- May 27th 2010, 03:55 PMpickslides
Here's a little more.

$\displaystyle \cos^{4}x-\cos^{2}x \sin^{2}x+\sin^{4}x$

$\displaystyle \cos^{2}x\cos^{2}x-\cos^{2}x \sin^{2}x+\sin^{4}x$

$\displaystyle (1-\sin^2{x})(1-\sin^2{x})-(1-\sin^2{x}) \sin^{2}x+\sin^{4}x$

Now expand this.