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Using trigonometric identities, show that (cos(x) + sin(x))^2=1+sin(2x)

First being by expanding the brackets of the formula on the left: (cos(x) + sin(x)) 2 = (cos(x) + sin(x))*(cos(x) + sin(x)) = cos 2 (x)+2cos(x)sin(x)+sin 2 (x).Now we must use our understanding of trigonomet...
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differentiate tanx

tanx = sinx/cosxapply the quotient rule use the identity cos^x + sin^x = 1 to simplify
AM
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If the quadratic equation kx^2+kx+1=0 has no real roots, what values of k are possible?

The solutions to quadratic equations, which are of the form ax^2+bx+c=0 with a≠0, are given by the Quadratic Formula: x= [-b+-sqrt(b^2-4ac)]/(2a). However, all real numbers, whether negative or not, square t...
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Sketch the graph y = 2sin(4x)

We know that y=sinx is the sinusoidal graph that starts at the origin, with maxima at x = pi/2 with a value of 1, and a minima at x = 3pi/2 with a value of -1. The 4x inside the bracket means that all x valu...
GK
Answered by Gagan K. • Maths tutor
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Use calculus to find the set of values of x for which f(x) = x^3 - 9x is an increasing function.

f(x) is an increasing function when its gradient is positive. To find the the gradient of the the function we must differentiate it:d/dx f(x) = 3x 2 - 9. To differentiate we multiply the exponent by the coef...
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