IfA=340°, prove that
2sinA/2 = -(v1+sinA) + (v1-sinA)
To prove the given equation, we need to manipulate the equation using trigonometric identities and properties. Let's break it down step by step.
1. Start with the left-hand side of the equation: 2sin(A/2).
Here, we'll make use of the half-angle identity for sine: sin(A/2) = ± √((1-cosA)/2), where the sign depends on the quadrant of angle A.
Since A = 340°, it lies in the fourth quadrant, where sinA is negative. Thus, sin(A/2) = -√((1-cosA)/2).
Substitute this back into the original equation:
2sin(A/2) = 2 * (-√((1-cosA)/2))
2. Simplify the right-hand side of the equation: -(v1+sinA) + (v1-sinA).
Start by expanding the equation:
-(v1 + sinA) + (v1 - sinA) = -v1 - sinA + v1 - sinA
The v1 terms cancel each other out, leaving:
-sinA - sinA = -2sinA
3. Now, compare the derived left-hand side and the simplified right-hand side.
2sin(A/2) = -2sinA
Since the two sides of the equation are equal, we have successfully proven the given equation.
2sin 170° = .3472
sin 340° = -.3420
-√(1-.3420) + √(1+.3420)
= 1.1584 - .8112
= .3472