Question

3 cosA  = 4 sinA 

Evaluate 

Cosec²A  - 1/ tan ² A​

Answer 1

Step-by-step explanation:

$3 \: cos \: A \: = 4 \: sin \: A \\ \frac{3}{4} = \frac{sinA}{cosA} \\ \frac{3}{4} = tanA$

$P = 3 \: and \: B = 4 \\ {H}^{2} = {P}^{2} + {B}^{2} \\ {H}^{2} = {3}^{2} + {4}^{2} \\ {H}^{2} = 9 + 16 = 25 \\ H = 5$

$cosecA = \frac{H}{P} = \frac{5}{3}$

$\frac{ {cosec}^{2}A - 1 }{ {tan}^{2} A} = \frac{ { (\frac{5}{3}) }^{2} - 1}{ (\frac{3}{4})^{2} }$

$= \frac{ \frac{25}{9} - 1}{ \frac{9}{16} } \\ = \frac{ \frac{16}{9} }{ \frac{9}{16} } \\ = \frac{16}{9} \times \frac{16}{9} \\ = \frac{256}{81}$

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Answer 2

Answer:

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