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This question requires us to make use of the trigonometric identities tan(y)=sin(y)/cos(y) and sin^2y + cos^2y = 1 which are given in the formula sheet of the exam. Since we know that sin(y)/cos(y) can be...

y(x+y)=3,yx +y² =3,Differentiating with respect to x,y+x(dy/dx) +2y(dy/dx)=0when y=1, x=3-1=2 (from original equation)1+2(dy/dx) +2(dy/dx)=0,dy/dx=-1/4

This question makes use of the sin addition formula. It may be stated as sin (A + B) = sinA cosB + sinB cosA . We want to rewrite 2 cosx + 4 sinx in the form R sin (x + a), so firstly work out what R sin(...

If the function is even, f(x) = f(-x).cos(-x) is the same value as cos(+x) therefore the function is even. Its graphical property is that it is symmetrical about the y axis as all even functions are.

Chain rule: First resolve the log differential, then resolve the fraction integration either by knowing the formula for it or by writing (e^x+1)/(e^x-1) as (e^x+1)(e^x-1)^(-1) and applying chain rule agai...