Question

Given : 4 cot A = 3, find,
1.sin A
2. sec A
3.cosec²A - cot²A.​

Answer 1

Step-by-step explanation:

4 cot A = 3

cot A = 3/4

base / perpendicular = 3/4

base = 3

perpendicular = 4

Hence,

hypotenuse = 5

sin A= perpendicular / hypotenuse

sin A =4/5

sec A = hypotenuse/ base

sec A = 5/3

by identity of trigo...

cosec^2 - cot ^2 = 1

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Answer 2

(1) 4/5

(2) 5/3

(3)  -81/400

Step-by-step explanation:

4 cot A = 3

cot A = $\frac{3}{4}$

By using pythagoras theorem

(1) sin A = $\frac{p}{h} =\frac{4}{5}$

(2) sec A = $\frac{h}{b}=\frac{5}{3}$

(3) $cosec^2$ A - $cot^2$ A

$(\frac{b}{h} )^2-(\frac{b}{p})^2\\(\frac{3}{5})^2-(\frac{3}{4})^2\\\frac{9}{25}-\frac{9}{16}$

After L.C.M

we get,

$\frac{-81}{400}$