Question

If sin@-cos@ = 1/2
Then find the value of 1/ sin@ + cos @

Answer 1

Sin^2a + Cos^2a=1

Cos^2a=1-Sin^2a

Sin^2a + Cos^2a - 2SinaCosa= 1/4      (squaring the given eqn)

1-Sin2a=1/4

3/4=2sina cos2----------------------------------------(1)

(Sina + cosa)^2=1+2sinacosa = 7/4

sina +cos a = sqrt(7)/2