4.
tan [ arcsin (-1/2) ]
________________
cos [ arctan (1)]
Let arcsin (-1/2) = A and arctan (1) = B .....so we have
tan (A)
______
cos (B)
If arcsin (-1/2) = A....rhis angle is a Q4 angle....x will be positive here
Then x = sqrt [ 4 - 1 ] = sqrt (3)
So tan (A) = -1/ sqrt (3)
If arctan (1) = B.......this is a Q1 angle
r= sqrt (1 + 1 ) = sqrt (2)
So cos B= 1/ sqrt (2)
So we have
(-1/sqrt (3) )
__________ =
( 1/sqrt (2))
-sqrt (2) /sqrt (3) =
- sqrt (6) / 3