If x-a sin A and y-b tan A- then prove that a2x2-b2y2-1

LHS : a^2x^2 b^2y^2 =a^2a^2 sin^2 A b^2b^2 tan^2 A =1sin^2 A 1tan^2 A =cosec^2 A cot^2A=1 = RHS ...

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Trigonometric Equations

If x=a sin ...

Question

If $x = a sin A$ and $y = b tan A$ , then prove that $\frac{a^{2}}{x^{2}} - \frac{b^{2}}{y^{2}} = 1$

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If x = a cos A - b sin A and y = b cos A + a sin A, prove that x² + y² = a² + b² .

x = a sin θ

y = b tan θ

\frac{a^{2}}{x^{2}} - \frac{b^{2}}{y^{2}} = 1

x = a sin θ + b cos θ

y = a cos θ - b sin θ

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

x = a sec θ cos ϕ, y = b sec θ sin ϕ

z = c tan θ

(\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}) = (1 + \frac{z^{2}}{c^{2}})

θ

θ

\frac{a^{2}}{x^{2}} - \frac{b^{2}}{y^{2}} = 1

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