4 A = 3 A = 3/4 = B/P P = 4 , B = 3 Now, H^2 = P^2 + B^2 H^2 = 3^2 + 4^2 H^2 = 5^2 H = 5 cosec^2 A cot^2 A nbs ...

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Circular Measurement of Angle

cosec2 A - co...

Question

$c o s e c^{2} A - c o t^{2} A$ .

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Solution

$4 cot A = 3$
$cot A = \frac{3}{4} = \frac{B}{P}$
$P = 4$ , $B = 3$
Now, $H^{2} = P^{2} + B^{2}$
$H^{2} = 3^{2} + 4^{2}$
$H^{2} = 5^{2}$
$H = 5$
$c o s e c^{2} A - c o t^{2} A = (\frac{H}{P})^{2} - (\frac{B}{P})^{2}$
= $(\frac{5}{4})^{2} - (\frac{3}{4})^{2}$
= $\frac{25}{16} - \frac{9}{16}$
= $\frac{16}{16}$
= $1$

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c o s e c^{2} A = 1 + c o t^{2} A

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