To find the value of the expression (2sin a + sin^2 a) / (2sin a - sin^2 a) when cos a = 1/5, we first need to find the value of sin a using the Pythagorean identity sin^2 a + cos^2 a = 1.
Given that cos a = 1/5, we can calculate sin a as follows: sin^2 a + (1/5)^2 = 1 sin^2 a + 1/25 = 1 sin^2 a = 24/25 sin a = sqrt(24/25) sin a = 2sqrt(6) / 5
Now we can substitute the values of sin a and cos a into the expression:
(2sin a + sin^2 a) / (2sin a - sin^2 a) = (2(2sqrt(6)/5) + (2sqrt(6)/5)^2) / (2(2sqrt(6)/5) - (2sqrt(6)/5)^2)
To find the value of the expression (2sin a + sin^2 a) / (2sin a - sin^2 a) when cos a = 1/5, we first need to find the value of sin a using the Pythagorean identity sin^2 a + cos^2 a = 1.
Given that cos a = 1/5, we can calculate sin a as follows:
sin^2 a + (1/5)^2 = 1
sin^2 a + 1/25 = 1
sin^2 a = 24/25
sin a = sqrt(24/25)
sin a = 2sqrt(6) / 5
Now we can substitute the values of sin a and cos a into the expression:
(2sin a + sin^2 a) / (2sin a - sin^2 a) = (2(2sqrt(6)/5) + (2sqrt(6)/5)^2) / (2(2sqrt(6)/5) - (2sqrt(6)/5)^2)
= (4sqrt(6)/5 + 24/25) / (4sqrt(6)/5 - 24/25)
Simplify the numerator:
= [(100sqrt(6) + 24) / 25] / [(100sqrt(6) - 24) / 25]
To divide by a fraction, multiply by the reciprocal:
= [(100sqrt(6) + 24) / 25] * [25 / (100sqrt(6) - 24)]
= (100sqrt(6) + 24) / (100sqrt(6) - 24)
Therefore, (2sin a + sin^2 a) / (2sin a - sin^2 a) = (100sqrt(6) + 24) / (100sqrt(6) - 24) when cos a = 1/5.