If A is an acute angle and cot A + cosec A = 3, then the value of cos A is equal to:

$\frac{4}{5}$

cot A + cosec A = 3   -------(1)

We know ,

cosec A - cot A =  \(\frac{1 }{cot A + cosec A }\) =  \(\frac{1 }{3 }\)  -----(2)

Adding equation 1 and 2.

2 cosecA = 3 + \(\frac{1 }{3 }\) = \(\frac{10 }{3 }\)

cosecA = \(\frac{5}{3 }\)

H² = P² + B²

5² = 3² + B²

B = 4

Now ,

cosA = \(\frac{B}{H}\) = \(\frac{4}{5 }\)