Math - A level

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sweetescobar
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#1
Report Thread starter 3 months ago
#1
How do I prove this identity:

(cosx + 3sinx)^2 is equivalent to 5-4cos2x + 3sin2x?

I managed to get the 3sin2x by doing 3(2sinxcosx) which is just 3sin2x and managed to get 10-9cos2x but as you can see its 5 -4cos2x...
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mqb2766
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#2
Report 3 months ago
#2
(Original post by sweetescobar)
How do I prove this identity:

(cosx + 3sinx)^2 is equivalent to 5-4cos2x + 3sin2x?

I managed to get the 3sin2x by doing 3(2sinxcosx) which is just 3sin2x and managed to get 10-9cos2x but as you can see its 5 -4cos2x...
Can you upload your working? It should be just a case of mapping the squared terms to double angles.
Last edited by mqb2766; 3 months ago
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davros
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#3
Report 3 months ago
#3
(Original post by sweetescobar)
How do I prove this identity:

(cosx + 3sinx)^2 is equivalent to 5-4cos2x + 3sin2x?

I managed to get the 3sin2x by doing 3(2sinxcosx) which is just 3sin2x and managed to get 10-9cos2x but as you can see its 5 -4cos2x...
As advised, post your working! What other terms do you get to combine apart from the 6cosxsinx term when you expand the bracket, and what double angle identities do you know?
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