Question

is sin bracket a + b bracket close is equals to 1 and Cos bracket a minus b bracket close is equals to 1, find a and b

Answer 1

As the examples showed, sometimes we need angles other than 0, 30, 45, 60, and 90 degrees. In this chapter you need to learn two things: 
1. Sin(A + B) is not equal to sin A + sin B. It doesn't work like removing the parentheses in algebra. 
2. The formula for what sin(A + B) does equal.

First to show that removing parentheses doesn't "work." Here: make A 30 degrees and B 45 degrees.

Sin 30 is 0.5. Sin 45 is 0.7071. Adding the two is 1.2071.

You know that no sine (or cosine) can be more than 1. Why? the ratio has the hypotenuse as its denominator. The most that the numerator can be is equal to the denominator. A sine or cosine can never be greater than 1, so a value of 1.2071 must be wrong. 

Wanted sine, cosine, or tangent, of whole angle (A + B)

Finding sin(A + B)

The easiest way to find sin(A + B), uses the geometrical construction shown here. The big angle, (A + B), consists of two smaller ones, A and B, The construction (1) shows that the opposite side is made of two parts. The lower part, divided by the line between the angles (2), is sin A. The line between the two angles divided by the hypotenuse (3) is cos B. Multiply the two together. The middle line is in both the numerator and denominator, so each cancels and leaves the lower part of the opposite over the hypotenuse