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Principal Solution of Trigonometric Equation

If asin θ +...

Question

If $a sin (θ + α) = b sin (θ + α)$ show that $cot θ = \frac{a cos α - b cos α}{b sin α - a sin α}$ .

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a sin (θ + α) = b sin (θ + β)

cot θ = \frac{a cos α - b cos β}{b sin β - a sin α}

a sin α, - b cos α

- a cos α, b sin α

a sin α, - b cos α

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(a sin α, - b cos α)

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A

θ = α

(x - a)^{2} + (y - b)^{2} = r^{2}

(x - a) cos α + (y - b) sin α = r

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