Question

Why is cos2x the answer of -sin^2x + cos^2x?

Answer 1

I tried this....hope it helps!

Explanation:

You know that `sin^2(x)+cos^2(x)=1`
so rearranging:
`sin^2(x)=1-cos^2(x)`

substituting into your expression you get:

`-1+cos^2(x)+cos^2(x)=2cos^2(x)-1`

Now let us choose an angle `x`, say `pi/3`:
we have:
`2cos^2(x)-1=2cos^2(pi/3)-1=2*(1/2)^2-1=-1/2`
or:
`cos(2x)=cos(2pi/3)=-1/2`
You can try with other angles to see it!!!

Answer 2

See below

Explanation:

Use the Property:`cos(A+B)= cosAcosB-sinAsinB`
Left Side:`cos 2x= cos(x+x)=cosx cosx -sinx sinx`

`=cos^2x-sin^2x`

`=`Right Side