Trig Identity Q (1 Viewer)

buitifulpeople · Sep 12, 2014

Hey guys,

So in prelim today we had a question to show:

sin^2 (5x) - sin^2 (3x) = sin(8x) . sin(2x)

What I did was pretty much prove sum to product formula and then used it. But seeing as it's not in the syllabus, how would someone do this within the confines of the 3U syllabus?

What I did: http://puu.sh/bvqZ2/ac92165edc.png

Thanks in advance.

Drongoski · Sep 12, 2014

buitifulpeople said:
Hey guys,

So in prelim today we had a question to show:

sin^2 (5x) - sin^2 (3x) = sin(8x) . sin(2x)

Essentially the same thing. RHS

$= sin(5x+3x)\cdot sin(5x-3x)\\ \\ = [sin5xcos3x + cos5xsin3x]\cdot[sin5xcos3x - cos5xsin3x] \\ \\ = (sin5xcos3x)^2 - (cos5xsin3x)^2\\ \\ = sin^2{5x}cos^2{3x} - cos^25xsin^2{3x} \\ \\ = sin^2{5x}(1-sin^2{3x}) - cos^2{5x}sin^2{3x} \\ \\ = sin^2{5x} - sin^2{3x} (sin^2{5x} + cos^2{5x}) \\ \\ = sin^2{5x} - sin^2{3x}$

= LHS

PS

Just curious. Why must you kids begin your blurbs with a So?

Trig Identity Q (1 Viewer)

buitifulpeople

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Drongoski

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