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Using the trigonometric identity for tan(A + B), prove that tan(3x)=(3tan(x)-tan^3(x))/(1-3tan^2(x))

tan(3x)=tan(2x+x), by using the identity for tan(A+B)=(tan(A)+tan(B))/(1-tan(A)tan(B)),tan(3x)=tan(2x+x)=(tan(2x)+tan(x))/(1-tan(2x)tan(x)), using it again for tan(2x),tan(3x)=tan(2x+x)=([(tan(x)+tan(x))/...

Answered by Ivan R. • Maths tutor

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a curve is defined by y=2x^2 - 10x +7. point (3, -5) lies on this curve. find the equation of the normal to this curve

equation of tangent is y - y1 = m(x-x1). differentiating y gives us the value of m. so dy/dx = 4x-10. we know x is 3. therefore, dy/dx = m = 2 but we need equation of the normal, which is y-y1=(1/m)(x-x1)...

Answered by Huy H. • Maths tutor

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The curve C has an equation y = sin(2x)cos(x)^2. Find dy/dx. Find normal to curve at x = pi/3 rad, giving answer in exact form.

Student should use a combination of trigonometric identities, product rule and chain rule to find dy/dx.This can be done by applying product rule, obtainingdy/dx = sin(2x). d[cos(x)^2]/dx + cos(x)^2. d[si...

Answered by Sunchi C. • Maths tutor

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Solve the equation 3 sin^2 theta = 4 cos theta − 1 for 0 ≤ theta ≤ 360

I would convert the sin squared theta into a cos squared theta using identity that sin sq + cos sq = 1This would then give me a quadratic equation which I would substitute X = cos thetaThen I would solve ...

Answered by Mario L. • Maths tutor

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The circle C has centre (3, 1) and passes through the point P(8, 3). (a) Find an equation for C. (b) Find an equation for the tangent to C at P, giving your answer in the form ax + by + c = 0 , where a, b and c are integers.

A)1) Draw a diagram of the circle displaying the centre and perimeter points along with their respective co-ordinates.2) Write down the equation for a circle labelling the centre and perimeter points. 3) ...

Answered by Patrick V. • Maths tutor

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