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Prove: (3cosx + 4sinx)^2 + (4cosx - 3sinx)^2=5 ...this is all under the square root sign.

this is what i did please check.
i multipied both binomials. but i get cos square x..and sincosx do i combine them..please help!

In this case, after multiplying binomials, there will be 24sincos and -24sincos terms that cancel. That will leave you with sin^2 and cos^2 terms. Write sin^2 as 1-cos^2 and solve for cosx

i get 9cos^2x + 16sin^2x +16cos^2x + 9sin^2x

now i know that sin^2 equals 1-cos^ would that be 9cos^2x + 17-cos^2x+16cos^2+ 10cos^2x? if not please help..and if this is correct..what would come after this step?

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