The answer can be found immediately with a calculator. However since you are asking this, I am supposing you are asking to show why without using any numerical calculations. You can use only information about the signs in the various quadrants and the fact that an angle is increasing in QI A = 340° is in QIV and has reference angle 360°-340° = 20° thus sin(340°) = -sin(20°) A/2 = 170° is in QII and has reference angle 180°-170° = 10° thus sin(170°) = sin(10°) And we know that sin(20°) > sin(10°)) We put question marks for the signs + or - to include all choices A), B), C), D) 2sin(170°) = ? √(1+sin340°) ? √(1-sin340°) becomes: 2sin(10°) = ?√(1-sin(20°) ? √(1+sin(20°) Since √(1+sin(20°) has the larger absolute value it must be positive. So B) and C) are eliminated. 2sin(10°) = ?√(1-sin(20°) + √(1+sin(20°) We square both sides: 4sinē(10°) = 1 -sin(20°) ? 2√(1-sin(20°))√(1+sin(20°)) + 1+sin(20°) Note that the ? did not change in the squaring process. 4sinē(10°) = 2 ? 2√(1-sinē(20°)) 2sinē(10°) = 1 ? √cosē(20°) 2sinē(10°) = 1 ? √cosē(20°) There is an Identity which states:thus Therefore the ? must be - Therefore the only correct choice is D). Edwin