# How do you simplify #sin[Tan^-1 (-2/5) + Cos^-1 (3/5)]#?

##### 1 Answer

#### Explanation:

Let

So, principal a is in the 4th quadrant.

And so, sin is negative and cos is positive.

Thus, in this case,

Let

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