Question 253677
Let's take these one at at time:
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1.) if sin x= (12/13), cos y=(3/5) and x and y are acute angles, the value of cos(x-y) is
a.(21/65) b.(63/65) c. -(14/65) d. -(33/65)
We have two angles, x and y.
Sin(x) = 12/13.
using Pythagorean theorem, we can find 
cos(x) = 5/13.
Now,
Cos(y) = 3/5
using Pythagorean theorem, we can find 
sin(x) = 4/5.
Cos(x-y) has formula
{{{cos(x-y) = cos(x)*cos(y) + sin(x)*sin(y)}}}
when putting in our numbers, we get
{{{cos(x-y) = (5/13)*(3/5) + (12/13)*(4/5)}}}
which can be expressed as
{{{cos(x-y) = 15/(65) + 48/65}}}
{{{cos(x-y) = 63/(65)}}}
which is [B]
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2.) if the tangent of an angle is negative and its secant is positive, in which quadrant does the angle terminate

The tangent of x is negative in quadrant II and IV
The secant (1 /cos) of x is positive in I and IV.
They overlap in IV.
Terminate is just a fancy word for where the vertex of the triangle sits.