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Because in the triangle ABC, the angle ABC + angle C = 180 degrees - the angle A is bisected by AD
So 1 2 (angle abc + angle c) = 1 2 (180 degrees - angle a) = 90 degrees - because be perpendicular ac
So the angle bea = 90 degrees.
So angle 2 = 90 degrees - angle dac
So angle 2 = 1 2 (angle abc + angle c).
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Solution: The sum of the three angles of the triangle is 180 degrees, there is abc + bac + c = 180 so there is 1 2 ( abc + bac + c) = 90 so 1 2 ( abc + c) = 90-1 2 bac according to the title: in afe, fae = 1 2 bac; ∠aef=902=180-∠aef-∠fae=180-90-1/2∠bac=1/2(∠abc+∠c)
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Answer: 1 From the question, da=od*sinx=4sinxoa=od*cosx=4cosx
s=da*2oa=4sinx*8cosx=16sin2x, so s(x)=16sin2x
2 Since the value of sin2x is -1 to 1, when sin2x = 1, s(x) has a maximum value, at this time x = 45 degrees, and the maximum value of s(x) = 16
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Let the length of the rectangle be b and the width of the rectangle be a
1) s=ab=(4sinx)*2*4*cosx=16sin2x(2) When sin2x=1, that is, 2x=90°, when s max is x=45°, s max=16
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1. All are correct.
2、(1)∪ x∈(-0)∪(1,+∞2) x∈(-3)
3)∪ x∈(-2)∪(3/2,+∞4)∪ x∈(-3)∪(4,+∞5)∪ x∈(-2)∪(2,+∞6) x∈[-1,3]
7) No solution. 8) x (-1- 2) (1- 2,+ 3, (1) a> at 0 x>1 a a< at 0 x<1 a a=0 when there is no solution.
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Tangent, 3Intersect, secant, tangent, tangent, distancing.
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Intersecting, secant, tangent, tangent, tangent, distancing.
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