trig

[dcgirl]

How do you prove that sin^2x+2cos^2x-1=cos^2x and also how do you prove that 1/sin^2x+1/cos^2x=1/sin^2x-sin^4x

 

[Gene]

You know that sin²(x)+cos²(x)=1
Solve that for sin²(x) and substitute.

You have to buy a bunch of ()s to use. For
1/sin^2x+1/cos^2x=1/sin^2x-sin^4x
you mean
1/sin^2x+1/cos^2x=1/(sin^2x-sin^4x)
Put the LHS over a common denominator.
Factor the RHS and use sin²(x)+cos²(x)=1 twice more.

 

[dcgirl]

how do i factor the RS in the second question

 

[Gene]

sin^2(x)-sin^4(x) =
sin^2(x)(1-sin^2(x))

 

[dcgirl]

thanks