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Prove: (1-cos(2A))/sin(2A) = tan(A)

Firstly we must lay out our double angle formulas which are required for this question: cos(2A) = 1-2sin^2(A) = 2cos^2(A)-1 sin(2A) = 2sin(A)cos(A) Working from LHS: (1-cos(2A))/sin(2A) Focusing on the denom...
RP
Answered by Rishi P. • Maths tutor
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What is ln(10)-ln(5)?

Laws of logs tells us that ln(a) - ln(b) = ln(a/b) Therefore ln(10)-ln(5) = ln(10/5) = ln(2)
JC
Answered by Jawad C. • Maths tutor
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differentiate 4x^3 + 3x^2 -5x +1

when differentiating, we multiply the power by the coefficient and then take the power away by 1 so : y= 4x^3 + 3x^2 -5x +1 then 4 x 3= 12 and 3-1 = 2 meaning the solution is 12x^2. 2 x 3 = 6 and 2-1 = 1 giv...
JR
Answered by James R. • Maths tutor
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Use logarithms to solve the equation 2^(5x) = 3^(2x+1) , giving the answer correct to 3 significant figures

Taking the log of both sides we get 5x * ln2 = (2x+1) * ln3. Taking everything that contains x to the left side: x * (5 ln2 - 2 ln3) = ln3. Therefore x=ln3/(5 ln2 - 2 ln3) x is approx 0.866
BB
Answered by Beatrice B. • Maths tutor
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Find dy/dx of the curve x^3+5xy-2y^2-57=0

3x 2 +5y+5x(dy/dx)-4y(dy/dx)=0 3x 2 +5y=(5x-4y)dy/dx dy/dx=(3x 2 +5y)/(5x-4y)
SP
Answered by Steven P. • Maths tutor
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