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Prove that sin(x)+sin(y)=2sin((x+y)/2)cos((x-y)/2)

We know that 1. sin(a+b) = sin(a)cos(b)+sin(b)cos(a) and 2. sin(a-b) = sin(a)cos(b)-sin(b)cos(a) Add equations 1. and 2. sin(a+b)+sin(a-b) = 2sin(a)cos(b)+sin(b)cos(a)-sin(b)cos(a) = 2sin(a)cos(b) Let x=a+b ...
AV
Answered by Anna V. • Maths tutor
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The points A and B have coordinates (3, 4) and (7, 6) respectively. The straight line l passes through A and is perpendicular to AB. Find an equation for l, giving your answer in the form ax + by + c = 0, where a, b and c are integers.

For the line passing through A and B: m = (y2-y1)/(x2-x1) = (-6-4)/(7-3) = -5/2 For the perpendicular line: m = -1/(-5/2) = 2/5 y - y1 = m*(x - x1) >> y - 4 = (2/5)*(x - 3) >> 5y - 20 = 2x - 6 &g...
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Answered by Deji A. • Maths tutor
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Find the gradient of the tangent to the curve with the equation y = (3x^4 - 18)/x at the point where x = 3

y = (3x 4 - 18)/x The gradient of a tangent to a curve is equal to dy/dx However, we must simplify this equation before we can differentiate it; y = 3x 3 - 18/x = 3x 3 - 18x -1 dy/dx = 3(3x 2 ) - (-1)(18x -2...
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Answered by Rachel O. • Maths tutor
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Find the turning points of the curve y = x^3 +5x^2 -6x +4

y = x 3 +5 x 2 -6 x +4 dy/dx = 3 x 2 +10 x -6 at turning points dy/dx = 0 therefore 3 x 2 +10 x -6 = 0 This quadratic is factorisable. When factorised you get: (3 x -2)( x +4) = 0 therefore x = 2/3 and -4 at...
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Answered by Arshan B. • Maths tutor
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Differentiate y=x^3

dy/dx = 3x^2
RH
Answered by Rhiannon H. • Maths tutor
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