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Derivative of One Function w.r.t Another

17. If x=p se...

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17. If x=p sec Q+ q tan Q and y=p tan Q + q sec Q then prove that x2 -y2 =p2 - q2

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P = {sec}^{6} A - {tan}^{6} A

Q = 3 {sec}^{2} A {tan}^{2} A,

P - Q

x = p sec θ

y = q tan θ

\frac{sin A}{sin B} = p, \frac{cos A}{cos B} = q,

then prove that -

tan A = \pm \frac{p}{q} \sqrt{(\frac{1 - q^{2}}{p^{2} - 1})}, tan B = \pm \sqrt{(\frac{1 - q^{2}}{p^{2} - 1})}

P = \frac{x}{x + y}, Q = \frac{y}{x + y}

\frac{1}{P - Q} - \frac{2 Q}{P^{2} - Q^{2}}

p

q

are distinct reals , then

2 {(x - p) (x - q) + (p - x) (p - q) + (q - x) (q - p)} = {(p - q)}^{2} + {(x - p)}^{2}

+ {(x - q)}^{2}

is satisfied by

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Derivative of One Function w.r.t Another

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