Question

tanA=4/3, find cosec A/cot A-sec A​

Answer 1

Explanation:

the answer is -15/11

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Answer 2

Explanation:

we know that

tanA = (perpendicular)/(base)

So taking right angle triangle

using pythagoras theorem

(hypotenuse)^2= (perpendicular)^2 + (base)^2

h^2 = 4^2 +3^2

h^2 = 16 +9

h ^2 = 25

h = 5

Now cosecA = hypotenuse/ perpendicular

cosecA = 5/4

cot A = base/ perpendicular

cot A = 3/5

sec A = hypotenuse/ base

sec A=5/3

$\frac{cosec( A)}{ \cot( A) - \sec(A) } \\ = \frac{ \frac{5}{4} }{ \frac{3}{4} - \frac{5}{3} } \\ \\ = \frac{ \frac{5}{4} }{ \frac{9 - 20}{12} } \\ \\ = \frac{5}{4} \times \frac{ - 12}{11} \\ \\ = - \frac{15}{11}$