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Letting z be the complex number cos x + i sin x, we will use the identities (zⁿ + 1/zⁿ) = 2 cos nx and (zⁿ - 1/zⁿ) = 2i sin nx. Both of these follow from De Moi...

Set up the auxiliary equation by letting (dy/dx) = m
So we have: m² + 3m + 2 = 0
Solve for m and we get: (m+1)(m+2) = 0Therefore, m₁=-1 and m₂=-2
Now we s...

First we check the formula for our first case, n=1 where (cosx + isinx)ⁿ =cosnx + isinnx (cosx + isinx)¹ = cos(1x) + isin(1x) - holds true for n=1 next we assume true for our case n=...

okay so A is a 2x2 matrix.for it to be singular its determinate has to equal 0.a 2x2 matrix's determinate is equal to m_1,1m_2,2 - m_1,2m_2,1for this example:det(A)...

Since we are told that the line l is perpendicular to the line PQ, we first need to find out the gradient of PQ.
To do this, it is easiest to find out the co-ordinates of points P and Q in terms of...