This is the rule of sums of trig identities. It says that sin(a + b) = sina*cosb+sinb*cosa. Set up your right triangles. In a 30-60-90 triangle, the side across from the 60 angle is the square root of 3, the side across from the 30 is 1, and the hypotenuse is 2. In a 45-45-90 the sides across from the 45 degree angles are 1 and the hypotenuse is square root of 2. With that being said, the sin of 60 is

and the cos of 60 is 1/2. Both the sin and cos of 45 is

. So your formula is filled in like this:

. When you do the multiplication on those sets of parenthesis, you get

. When you add those your solution is

. Depending upon your instructor you may have to rationalize that denominator to get that radical out from under there, but if not, that's pretty much it!
Answer:
x = 13
y = 18.38
Step-by-step explanation:
tan 45 = x/13 (tangent = opposite / adjacent)
1 = x/13
multiply both sides by 13
x = 13
cos 45 = 13/y (cosine = adjacent / hypotenuse
0.7071 = 13/y
multiply both side by y
0.7071y = 13
divide both side by 0.7071
y = 18.38
Answer:
Function is decreasing on (-8,infinity)
Step-by-step explanation:
The given function is 
The first derivative is given by

For the function to be decreasing, we have

Divide both sides by -2. Since, we are dividing by a negative number hence, the inequality sign will change.

Subtract 8 to both sides

Therefore, the function is decreasing on (-8,infinity)
First option is correct.
Ok so do you have any idea how to start