(cos3x)^4+(sin3x)^4=cos(g(x)) find g(x)

If (e^x)(sin3x)=Im ((e^x)(e^i3x))integrate (e^x)(sin3x) I get the answer(e^x)(cos3x-3sin3x) +C My book gets the answer
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1.) How would I simplify: sin4x*cos3x -cos3x*sin3x into a single trigonometric function?2.) determine the general solution to
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(cos3x)^4+(sin3x)^4=cos(g(x))find g(x)
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(cos3x)^4+(sin3x)^4=cos(g(x))find g(x)
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(cos3x)^2+(sin3x)^2=cos(f(x))find f(x)
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(cos3x)^4+(sin3x)^4=cos(g(x))find g(x)
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cos4x*cos3x + sin4x*sin3x
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prove that cos3x+sin3x/cos x-sin x=1+2sin2x
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value of expression (cos5x + cos3x)/ (sin5x - sin3x) where x = (3.14/8)
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Prove: sin3x-sinx/cos3x-cosx=-cot2
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