Question

How do you simplify `cos(sin^-1(3/5)-cos^-1(1/2))`?

Answer 1

`(1/10)(+-4+-3sqrt3)`

Explanation:

Let `a = sin^(-1)(3/5) and b = cos ^(-1)(1/2)`.

Then, `sin a = 3/5, cos a = +-4/5, cos b = 1/2 and sin b = +-sqrt3 /2`

Now, the given expression is `cos (a - b )`

`= cos a cos b + sin a sinb`

`=+-2/5+-3sqrt3/10=(1/10)(+-4+-3sqrt3)`.

The choice of sign depends on the specified ranges (if any ), for the inverse angles.a and b.