If cot A= 5/12 , find the value of the following expression. (5(1-cos² A))/(6(1-sin² A))

If cot A= 5/12 , find the value of the following…

If cot A= $\frac{5}{12}$ , find the value of the following expression.

$\frac{5(1-cos^2 A)}{6(1-sin^2 A)}$

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. $\frac{24}{5}$ .

cot A = Base/Length = 5/12

Hypotenuse = √(5² + 12²) = √(25 + 144) = √169 = 13

Now, $\frac{5(1-cos^2 A)}{6(1-sin^2 A)}$

= [5(1 - (5/13)²)]/[6(1 - (12/13)²)]

= [5(1 - 25/169)]/[6(1 - 144/169)]

= [5(144/169)]/[6(25/169)]

= 720/150

= 24/5

Therefore, the value of the expression is 24/5.