hello, i was wondering if anyone could help me!

i am stuck on a particular question with my maths homework set over the holidays. can you help with this: simplify and express with no denominator

(1/sqrt(x) -sqrt(x))^2

(1 over square root of x - square root of x) all squared

i am also stuck on this one: 2cos^2x - 1 = 1-2sin^2 x

please help, i am rather confused :S

## homework help

### Physics and Maths Tutor

Posted 29 August 2010 - 10:56 PM

(a-b)^2 = a^2 + b^2 - 2ab

so, (1/sqrt(x) -sqrt(x))^2 = 1/x + x - 2*(1/x)*x = x + 1/x - 2

cos^2x = 1 - sin^2 x

so, 2cos^2x - 1 = 2(1-sin^2 x) - 1 = 2 - 2sin^2 x - 1 = 1 - 2sin^2 x

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so, (1/sqrt(x) -sqrt(x))^2 = 1/x + x - 2*(1/x)*x = x + 1/x - 2

cos^2x = 1 - sin^2 x

so, 2cos^2x - 1 = 2(1-sin^2 x) - 1 = 2 - 2sin^2 x - 1 = 1 - 2sin^2 x

Edinburgh Physics and Maths Tutor

www.physics-maths.co.uk

tutor@physics-maths.co.uk

My link