Find the exact value of cos(a + b), given sin a = 2/5 for a in Quadrant || and cos B = 1/3 for b in Quadrant IV.

Option (4)

Step-by-step explanation:

cos(a + b) = cos(a)cos(b) - sin(a)sin(b) [Identity]

Since, sin(a) = for a in quadrant II

Therefore, cos(a) =

cos(a) =

But cosine of a is negative quadrant II

Therefore, cos(a) = -

And cos(b) = for b in quadrant IV

Therefore, sin(b) =

                           =

                           =

But sine of an angle is negative in quadrant IV,

Therefore, sin(b) =

Now substituting these values in the identity,

cos(a + b) =

                =

                =

Therefore, Option (4) will be the answer.