it all began with a simple joke that triggered my own ego – i got an A for C maths, why wouldnt i be able to handle A maths? i had to challenge myself, more to let myself know that i still had maths genes in me!
granted, being away from A/C maths for more than a decade, i needed the formula sheets and some trial and errors… and after ONE WHOLE HOUR at the question, i finally did it. and quite frankly, that light you see when you reach the step before the final answer – that light is one joyous bright light.
question was to write f(x)=10cos^2 x -8sinxcosx +4sin^2 x –> Acos2x + Bsin2x + C, where A, B, C are constants.
i looked at the question and thought, “crap! where do i even start!!?!?!?!?!”
slowly, i figured it out. and while the question might be easy to anyone doing A/C maths now, after more than a decade, sometimes i think i still have it in me man… hehehe…
y=10cos^2 x -8sinxcosx +4sin^2 x
y=10cos^2 x – 4sin2x +4sin^2 x
y=10c0s^2 x +4sin^2 x -4sin2x
y= 6cos^2 x + 4cos^2 x +4sin^2 x – 4sin2x
y=6cos^2 x + 4(cos^2 x + sin^2 x) – 4sin2x
y=6cos^2 x +4(1) – 4sin2x
y=6(1-sin^2 x) + 4 – 4sin2x
y=6-6sin^2 x + 4 – 4sin2x
y=10 – 6sin^2 x – 4sin2x
y=7 + 3 – 6sin^2 x – 4sin2x
y= 7 + 3(1-2sin^2 x) – 4sin2x
y=7 + 3cos2x – 4sin2x
therefore y=3cos2x -4sin2x + 7, where A = 3, B = -4 and C = 7
wow…………………. euphoria! ive not felt this way abt maths in a reaaaaaallllllllyyyyyyy long time! the feeling you get when you see the pattern is just everything i needed to brighten up my day! 😀 shiok!
nice job TJ and Valentino… it was fun with these 2 ppl who were also very determined to solve this useful-only-till-Os question.