Range of asin x-bcos x-a2-b2-a2-b2-

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Methods of Solving Trigonometric Equations: By Introducing Auxiliary Angle

Range of asin...

Question

Range of $a sin x + b cos x = [- \sqrt{a^{2} + b^{2}}, \sqrt{a^{2} + b^{2}}] ?$

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\tan x = \frac{a}{b},

\frac{a \sin x - b \cos x}{a \sin x + b \cos x} = \frac{a^{2} - b^{2}}{a^{2} + b^{2}}

- \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 = \frac{2 c tan x}{1 - {tan}^{2} x}

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

k =

f (x) = sin x - cos x

[- \sqrt{2}, \sqrt{2}]

g (x) = a sin x + b cos x

[- \sqrt{a^{2} + b^{2}}, \sqrt{a^{2} + b^{2}}]

f (x) = sin x - cos x

g (x)

a sin x + b cos x = c

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

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