IIT JEE , AIEEE Forum - Mathematics , Trignometry

prateek.agarwal

Its a multiple correct question...

The answers are (A) & (B)

KAB

root(1-sinA)=sin(A/2)-cos(A/2) when sin(A/2)>cos(A/2)

When A/2 lies in 1st quadrant and pi/4<A/2<pi/2 ,sin(A/2)>cos(A/2)
So A/2-pi/4 lies in 1st quadrant

When A/2 lies in 2nd quadrant,A/2-pi/4 may lie in 2nd or 1st quadrant.

When A/2 lies in 3rd quadrant sin(A/2) and cos(A/2) both are negative.
Also when pi<A/2<5pi/4 sin(A/2)>cos(A/2)

So 3pi/4<A/2-pi/4<pi which is in 2nd quadrant.

So the correct answers are A) and B)

newarnav

Thats an Identity and valid for every real A