How do you simplify #sin[Tan^-1 (-2/5) + Cos^-1 (3/5)]#?
So, principal a is in the 4th quadrant.
And so, sin is negative and cos is positive.
Thus, in this case,
So, principal b is in the 1st quadrant.
And so, sin is positive..
Thus, in this case, sin b = 4/5.
The given expression = sin (a + b)=sin a cos b+cos a sin b
In general, a is in either 4th quadrant or in the 2nd and b is in either
1st or the 2nd. So, sin a and cos a can take both signs.
ln general, b is in either 1st or 4th. So, sin b can take both signs.
Accordingly, the general values are