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Firstly, xcos(x) is a product of two functions of x. Therefore we can use the product rule to work out the derivative of the whole function. Differentiating each part makes it easier to visualize the ...
Cosec2A - cot2A= tanALeft hand side=1/sin2A - cos2A/sin2A=(1- cos2A)/sin2A=(1-(1- 2 sin^2 A)/ 2sinAcosA=(1-1 + ( 2 sin^2 A))/ 2sinAcosA=sinA/cosA=tanATherefore ...
dy/dx = (dy/dt)/(dx/dt) y = t(4-t2 ), then using differentiation of y with respect to t, dy/dt = 4 - 3t2x = t2 + 2, then...
Start by expanding out Rsin(2x+a) using the addition formula for sin, sin(A+B) = sin(A)cos(B)+cos(A)sin(B). Substituting 2x = A and a= b, we get that Rsin(2x+a) = R(sin(2x)cos(a) + cos(2x)sin(a)) = Rcos(a...
We already have an expression for y, so we can substitute this in:x2+(x+1)2=x2+(x+1)(x+1) = x2+x2+2x+1=2x2+2x+1 and hence 2x2+2...
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