Question

if sec a + tan a =2, then the value of sin a is (assume that 0 < a < 90°)​

Answer 1

Answer:

Sin a = 0.6

Step-by-step explanation:

Sec a + tan a = 2

1/cos a + sin a / cos a = 2

taking LCM on LHS

1 + sin a / cos a = 2

1 + sin a = 2 cos a

squaring both side

(1 + sin a)² = (2 cos a)²

1 + sin² a + 2 sin a = 4 cos² a

1 + sin² a + 2 sin a = 4( 1- sin² a)

1 + sin² a + 2 sin a = 4 - 4 sin² a

5 sin² a + 2 sin a - 3 = 0

factorising by middle term splitting method

5 sin² a + (5-3) sin a - 3 = 0

5 sin² a + 5 sin a - 3 sin a -3 = 0

5 sin a ( sin a + 1) - 3 ( sin a + 1) = 0

(5 sin a - 3) ( sin a + 1)

if a < 90°

5 sin a - 3

5 sin a = 3

sin a = 3/5

sin a = 0.6

Hope it will be helpful to you.....!!!!!

Plz mark it as Brainliest Answer...!!!!