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1. ### Trigonometry?

... to "solve" the equation, instead of "proving" it. LHS = (csc A + cot A) (1 − cos A) − (sec A + tan A...

5 Answers · Science & Mathematics · 08/01/2018

2. ### prove cos(x) - sec(x) = -tan(x) sin(x)?

secx = 1/cosx, so considering the LHS we have: cosx - (1/cosx) => (cos²x - 1)/cosx Now, sin²x...

4 Answers · Science & Mathematics · 04/01/2018

3. ### How will you prove that (√(4 - √7) = (√(8 + 3√7) - 2√2))?

L.H.S. = (√(4 - √7)) = (√7 - 1)/√2 R.H.S. = (√(8 + 3√7) - 2√2)) = (√7 - 1)/√2 Hence LHS = RHS

7 Answers · Science & Mathematics · 03/01/2018

4. ### (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

5. ### 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

6. ### 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

7. ### □ 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

8. ### 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

10. ### 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