For real a- b and x -a2-b2- a sin x - b cos x -a2-b2

Put a=r cos α, b=r sin α where r=√((a^2 + b^2)) ∴ a sin x + b cos x =r sin (x+α) since 1 ≤ sin θ≤ 1 therefore r ≤ sin(x + α) ≤ r etc ...

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Inequality

For real a, b...

Question

For real a, b and x $- \sqrt{(a^{2} + b^{2})} \leq a s i n x + b c o s x \leq \sqrt{(a^{2} + b^{2})}$

True

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False

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

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