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1. ### (6)　show : (sinx + acosx)(sinx + bcosx) ≤ 1 + [(a + b)/2]² .?

LHS = sin²x + (a+b)sinxcosx + abcos²x = ½{ (1+ab) + (a+b...2x) = √{(a+b)²+(ab−1)²}sin(2x+α) where tanα = (ab−1)/(a+b) ∴ LHS ≤ = ½{ (1+ab) + √{(a+b)²+(ab−1)²} } since sin≤1...

1 Answers · Science & Mathematics · 30/12/2017

2. ### 丁卯　show : a/(1 - a²) + b/(1 - b²) + c/(1 - c²) = 4abc/[(1 - a²)(1 - b²)(1 - c²)].?

LHS = { a(1−b²)(1−c²) + b(1−a²)(1−c²) + c(1...3w Numerator = wv−(uv−3w)+u = (w−u)(v−1)+4w = 4w since w=u ∴ LHS = 4abc/{(1−a²)(1−b²)(1−c²)}

1 Answers · Science & Mathematics · 27/12/2017

3. ### precalc problems?

...pi/6)-/+(pi/3) => k={[(-1)^k]-/+2} /6 The result is impossible for the LHS is an integer while the RHS is a fraction=> no integral k...

2 Answers · Science & Mathematics · 26/12/2017

4. ### □ show　a/√(a² + 8bc) + b/√(b² + 8ca) + c/√(c² + 8ab) ≥ 1　　　.?

... easy by Jensen using the convex function 1/√x (x>0) LHS is homogeneous so you can assume that a+b+c=1 and then apply Jensen with...

2 Answers · Science & Mathematics · 19/12/2017

5. ### Cos(A+B)cos(A-B) = cos^2 -sin^2B please show the workings in all areas for best answer?

LHS = cos(A+B) cos( A-B) =(cosAcosB - sinAsinB...

3 Answers · Science & Mathematics · 08/12/2017

LHS = 1 - [ (sin²x tanx ) / (tanx + 1) ] - [ cos²x / (tanx + 1) ] = [( tanx...

2 Answers · Science & Mathematics · 08/12/2017

7. ### verify the identity cot(x-pi/2)=-tan x?

LHS= cos(x-pi/2)/sin(x-pi/2)= [cos(x)*0+sin(x)*1]/ [sin(x)*0-cos(x)*1]= sin(x)/[-cos(x)]= -tan(x)= RHS.

4 Answers · Science & Mathematics · 12/01/2018

8. ### can someone help me with my math homework?

...(θ/2)) = |cos(θ/2)| = cos(θ/2) ..... since cos(θ/2) > 0 for 0 ≤ θ ≤ π = LHS

3 Answers · Science & Mathematics · 03/12/2017

9. ### Help with trig identities?

.../cosA 1 - sin²A = cos²A Starting with the LHS we have : ∴ LHS = [(secA + tanA) /(secA - tanA...

4 Answers · Science & Mathematics · 20/11/2017

10. ### Prove this trig identity?

LHS = (secA-cosA)/(cosA-sinA) = (1 - cos²A...

2 Answers · Science & Mathematics · 18/11/2017