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Firstly, you need to understand that the two equations are interlinked, therefore the x and the y variables are the same values in both equations. To make things easier, we can number both equations. What...

(sinx - tanx)(cosx - cotx)= (sinx - sinx/cosx)(cosx - cosx/sinx)= sinxcosx - (sinx + cosx) + 1= (sinx - 1)(cosx - 1)

sub y=kx-1 into circle equation, get (k^2+1)x^2-(8k+4)x+18=0for 2 distinct solutions need b^2-4ac>0, ie -8k^2+64k-56>0iff k^2-8k+7<0complete the square: intersections of equation in k satisfy(k-4...

base case: (1 x 2)/2 = 1 as required inductive step: assuming statement holds for n=k, the (k+1)th triangle number is given by k(k+1)/2 + (k+1) by definition=(k^2+3k+2)/2=(k+1)(k+2)/2=(k+1)((k+1)+1)/2resu...

Drawing this graph uses the same techniques as with most other functions. Just from inspection, we can see that as x increases, e^x also increases, and so the amplitude of the function will decrease (and ...