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Derivative of Some Standard Functions

If y= a sin 3...

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If y= a sin 3x + b cos 3x, prove that (d2y/dx2) + 4(dy/dx) + 3y= 10 cos 3x

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sin x + sin y = 3 (cos y - cos x)

sin 3 x + sin 3 y = 0

\frac{cos 4 x + cos 3 x + cos 2 x}{sin 4 x + sin 3 x + sin 2 x} = cot 3 x

(s i n 3 x + s i n x) s i n x + (c o s 3 x - c o s x) c o s x = 0

\int e^{3 x} c o s 4 x d x = e^{3 x} (A s i n 4 x + B c o s 4 x) + c

sin x + sin y = 3 (cos y - cos x)

, then the value of

sin 3 x + sin 3 y =

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