If asin3 x-b cos 3 x-sin x cos x and asin x-b cos x-0 prove that a2-b2-1

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First Fundamental Theorem of Calculus

If asin3 x+b ...

Question

If asin³x + bcos³x =sinxcosx and asinx-bcosx =0 prove that a²+b^{2 =}1

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a {sin}^{3} x + b {cos}^{3} x = sin x cos x

a sin x = b cos x

a, b, sin x

cos x

a^{2} + b^{2} =

a sin x = b cos x = \frac{2 c tan x}{1 - {tan}^{2} x}

(a^{2} - b^{2}) = k c^{2} (a^{2} + b^{2})

k =

- \sqrt{(a^{2} + b^{2})} \leq a s i n x + b c o s x \leq \sqrt{(a^{2} + b^{2})}

a sin x + b cos x = c

| c | > \sqrt{a^{2} + b^{2}}

y = A sin x + B cos x

\frac{d^{2} y}{d x^{2}} + y = 0

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