Algebraic Trigonometry

Algebra Level 3

If s i n x c o s x = 1 3 sin x - cos x = \frac{1}{3} . Find s i n 2 x sin 2x .

-1/2 1/2 -8/9 8/9

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1 solution

Peter Orton
Nov 22, 2014

sin x - cos x = 1/3. Squaring both side, (sin x)^2 - 2sin x cos x + (cos x)^2 = 1/9. Use identity, 1 - sin 2x = 1/9. And solve for sin 2x. Therefore, sin 2x = 8/9

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