Question

sin A - cos A = 1/2
Then find value of : 1/ sin A + cos A​

Answer 1

Sin a - cos a = 1/2

Squaring on both sides of the equation

(sin a) ^2 +(cos a) ^2 - 2 sin a cos a = 1/4

As we know that (sin a) ^2 +(cos a) ^2 = 1

1- 2 sin a cos a = 1/4

2 sin a cos a = 3/4 - - - 1⃣

(sin a + cos a) ^2 = (sin a) ^2 + (cos a) ^2 + 2 sin a cos a

As we know that (sin a) ^2 +(cos a) ^2 = 1

(sin a + cos a) ^2 = 1 + 2 sin a cos a

From above we got 2 sin a cos a = 3/4

so, (sin a + cos a) ^2 = 1 + 3/4

So, (sin a + cos a) ^2 = 7/4

(sin a + cos a) = (Sq.root 7) /