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To do this question we must first be aware of a few trigonometric identities. 1. sec(x) = 1/cos(x). 2. cos(A + B) = cos(A)cos(B) - sin(A)sin(B). (double angle formula) 3 . sin^2(x) = 1 - cos^2(x) Before d...

To begin, notice that the expression involves 2 functions of x multiplied together, this means we can approach the problem using integration by parts. Integration by parts can be expressed as '∫ u (dv/dx)...

Find the value of dx by dividing the difference between the integral boundaries by the number of ordinates minus 1. Therefore dx=(1-0)/4=1/4. Then define your ordinates, by 5 values between 0 and 1, where...

From the following identity, cos(a-b) = cosacosb+ sinasinb, we find that 4sinx+3cosx = R(cosxcosa+sinxsina). We now equate the coefficients: 3 = Rcosa and 4=Rsina. Using basic trigonometry, we can make th...

Firstly square both sides. This way, we now know that both sides have to be positive

(3x+1)^2 = 1

(3x+1)(3x+1) = 1

Expand the quadratic...

9x^2 + 12x + 4 = 1

9x^2 + 12x ...