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Math - A level

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...
Reply 1
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.
(edited 2 years ago)
Reply 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...

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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