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Help needed understanding higher 2001 maths question - HSN forum

# Help needed understanding higher 2001 maths question

### #1graham83

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Posted 06 April 2011 - 02:07 PM

The question is :

Show that f(h(x)) = 1/√2sinx+1/√2cosx

When f(h(x)) = sin(x+π/4)

I know the next step is sinxcosπ/4+cosxsinπ/4 but could someone tell me why this is and if there is some sort of formula used to arrive at this stage? Thanks

Graham

### #2Marcus

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Posted 06 April 2011 - 08:25 PM

graham83, on 06 April 2011 - 02:07 PM, said:

The question is :

Show that f(h(x)) = 1/√2sinx+1/√2cosx

When f(h(x)) = sin(x+π/4)

I know the next step is sinxcosπ/4+cosxsinπ/4 but could someone tell me why this is and if there is some sort of formula used to arrive at this stage? Thanks

Graham

it is from the sine expansion, sin(a + b) = sin(a)cos(b) + cos(a)sin(b) where a=x and b= π/4 I'm sure this is one of the formulae given in the exam (check a past paper to check) and from there sin(π/4)=cos(π/4)=1/√2 from your exact value triangles
=-=-=Marcus=-=-=

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